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UNIVERSITY  OF  CALIFORNIA. 


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A   PRACTICAL  TREATISE 

ON 

COMPRESSED  AIR 


AND 


PNEUMATIC 
MACHINERY 

BY 

EDWARD  A.  RIX  AND  A.  E.  CHODZKO 

(( 

PNEUMATIC  ENGINEERS 

FOR  THE 

FULTON 

Engineering  **  Shipbuilding  Works 


OFTHE          SAN    FRANCISCO 
UNIVERSITY 

OF 


MANUFACTURERS    OF 


MINING,    MILLING,    SMELTING    AND 
ELECTRICAL   MACHINERY 

ENGINES,  BOILERS,  HEATERS,  PUMPS,  ETC. 


MAIN  OFFICE  AND  BRANCH  WORKS,  213  FIRST  ST. 
MAIN  WORKS,  HARBOR  VIEW 

SAN   FRANCISCO,  CALIFORNIA 
1 80 


t 


Curves,  Tables  and  Engineering  Data  in  the  body 

of  this  Treatise  are  original  and  were 

prepared  by 

EDWARD  A.  R1X  AND  A.  E.  CHODZKO 

PNEUMATIC   ENGINEERS 

San  Francisco,    -     California 


Entered  according  to  Act  of  Congress,  in  the  year  1896, 

by 
THE  FULTON  ENGINEERING  AND  SHIPBUILDING  WORKS 

AND 

EDWARD   A.  RIX 

In  the  Office  of  the  Librarian  of  Congress, 
at  Washington,  D.  C. 


PKK»e  OF  IHK  UlCKM-JliDO  CO. 

•29  First  Street,  S»n  Francis 


'HE 

UNIVERSITY 


COMPRESSED  AIR. 


It  is  a  noteworthy  fact  that,  while  compressed  air  has  been 
known  and  been  used  at  a  time  when  dynamic  electricity  was 
not  even  in  its  infancy,  its  properties  and  possibilities  are  still, 
in  the  minds  of  many  practical  people,  an  object  shrouded  with 
confusion  and  mystery,  and  considered  by  them  as  a  convenient 
topic  for  the  scientist's  investigation,  but  altogether  too  intri- 
cate and  obscure  to  be  readily  grasped  by  a  man  possessed  of  a 
common  and  average  knowledge  of  motive  machinery. 

This  same  man,  strange  to  say,  will  find  no  apparent  mys- 
tery in  handling  a  first-class  Compound  Condensing  Steam 
Engine,  whose  thorough  comprehension,  however,  involves  a 
more  imposing  array  of  natural  phenomena  than  does  the 
action  of  an  air  motor. 

Mention  to  him  this  latter  machine,  and  he  will  tell  you  at 
once  that  it  is  useless;  he  has  a  vague  recollection  that  com- 
pressed air  will  not  yield  over  15  to  20  per  cent  of  the  power 
expended  to  produce  it,  while  an  electric  motor  utilizes  60  or 
80  per  cent  of  this  power,  and  that  is  the  end  of  it. 

The  fact  is,  however,  wiffooutin  any  way  disparaging  the 
wonderful  strides  made  by  electricity,  that,  in  a  great  many 
circumstances,  a  compressed  air  power  transmission  will  be 
found  fully  as  much,  and  often  more  effective  than  an  electrical 
transmission. 

Within  a  radius  of  10  to  20  miles  or  more,  it  is  not  a  matter 
of  theoretical  speculation,  but  a  result  of  actual  facts,  extend- 
ing over  a  period  of  many  years'  experience,  that  compressed 
air  can  be  economically  produced,  conveyed,  and  utilized  as  a 
motive  power;  and  if  this  power  is  to  be  distributed  through- 
out a  number  of  buildings  or  factories,  or  in  the  interior  of  a 
mine,  the  absolute  safety  consistent  with  the  use  of  compressed 
air  is  an  element  of  superiority  to  which  the  electrical  trans- 
mission has  no  possible  claim. 

However  well  insulated  the  conductors  may  be,  the  vicinity 
of  a  dynamo  is  always  dangerous,  either  on  the  ground  of  fire 
or  of  bodily  injury. 

In  a  large  power  station,  manned  by  a  picked  staff  of  attend- 
ants, this  danger  is  small  indeed;  but  the  conditions  are  alto- 
gether different  if  the  motor  is  under  the  care  of  a  miner  or  of 
an  ordinary  workman. 

Again,  the  location  of  an  air  motor  is  privileged  with  a  con- 
stantly renewed  and  wholesome  atmosphere,  whose  tempera- 
ture can  be,  at  will,  regulated  to  suit  the  local  exigencies. 

Accidental  circumstances  which  may  occur  in  the  vicinity 
of  an  electric  wire  under  high  potential  are  generally  fraught 
with  peril.  The  only  accident  to  which  an  air  pipe  is  liable  is 


4  COMPRESSED   AIR. 

a  leak,  which  will  cause  a  loss  of  power,  but  which  can  be  re- 
paired and  approached  at  no  risk  whatever. 

But  now  conies  another  point. 

Referring  more  especially  to  the  mines  which,  in  California, 
should  represent  a  large  percentage  of  the  users  of  compressed 
air,  an  example  will  well  illustrate  the  comparative  merits  of 
the  two  modes  of  power  transmission,  especially  for  mines. 

Take  a  mine  which  was  equipped  some  years  ago;  ample 
water  power  exists  several  miles  away,  but  the  configuration 
of  the  ground  did  not  permit  of  conveying  the  water  to  the 
mine;  a  telodynamic  transmission  would  not  have  been  practi- 
cal, so  the  owners  concluded  to  put  up  a  first-class  steam  plant 
for  hoisting,  pumping,  and  milling  purposes,  and  also  for  run- 
ning compressors  supplying  air  to  the  rock  drills,  and  perhaps 
to  one  or  more  underground  pumps  and  fans. 

In  the  course  of  time,  however,  timber  has  grown  scarce  in 
the  surrounding  sections,  and  now  they  have  to  haul  their  fire- 
wood at  the  rate  of  $5.00  or  $6.00  a  cord;  as  there  is  quite  an 
amount  of  power  used  at  the  mine,  this  represents  a  rather 
burdensome  item,  so  the  owners  begin  to  investigate  some  pos- 
sible way  out  of  it. 

An  electrical  transmission  is  forthwith  proposed  to  them, 
with  tangential  wheels  and  generators  near  the  waterfall,  con- 
ductors readily  spanning,  all  the  intervening  ridges  and  can- 
yons, and  a  number  of  dynamos  to  replace  the  steam  engines. 

It  is  a  practical,  feasible,  and  satisfactory  proposition,  but 
there  is  one  black  cloud  in  this  bright  sky:  what  shall  become 
of  the  steam  engines  and  boilers  ?  They  have  to  be  torn  down, 
of  course,  to  make  room  for  the  dynamos.  This  whole  plant 
is  still,  however,  in  perfect  condition;  it  has  been  bought, 
hauled,  and  erected  at  great  cost,  and  would  bring,  at  a  sale, 
about  as  much  as  its  equivalent  of  scrap  iron,  supposing  it 
could  be  sold  at  all.  The  proposed  plant  will  assuredly  be 
more  economical,  but  this  is  a  dead  loss  which  it  will  take  some 
time  to  make  up  for. 

Here  conies  the  opportunity  of  the  compressed-air  man;  he 
proposes  to  put  up  an  air-compressing  plant  at  the  water-fall; 
;the  iron-pipe  that  carries  the  air  will  span  ridges  and  canyons 
33  easily,  for  all  practical  purposes,  as  did  the  wires,  but  after 
'*&t  reaches  the  mine,  the  list  of  new  material  closes,  or  nearly 
so;  for  neither  the  engines  nor  the  boilers  will  have  to  be 
touched.  The  former  will  work  with  air  as  they  did  before 
with  steam,  the  boilers  being  used  for  heaters  or  air  receivers. 

The  compressor  that  used  to  work  at  the  mine  will  not  even 
have  to  be  discarded,  as  it  may  serve  either  as  a  reserve  or  as  a 
pressure  transformer;  in  other  words,  there  will  have  been  an 
addition  to  the  mine's  possessions,  in  the  shape  of  the  com- 
pressors at  the  power-house  and  of  the  pipes,  but  the  old  plant 
will  remain  just  as  it  was,  and  give  full  value  for  what  it  did 
cost;  it  will  simply  be  necessary  to  find  a  new  job  for  the  fire- 
men and  woodchoppers. 

Another  very  important  point:  suppose  the  power  plant  at 


COMPRESSED    AIR.  5 

the  water-fall  met  with  accident,  or  the  conductors  to  be  tem- 
porarily crippled;  with  the  electric  plant  it  means  a  stoppage  of 
the  whole  mine;  with  the  compressed  air  proposition  it  would 
only  be  necessary  to  fill  the  boilers,  start  up  the  fires,  and  run 
by  steam  again.  Here,  there  is  no  possible  competition  between 
the  two  systems.  The  advocates  for  electricity  claim  a  superior 
economy,  but  a  few  developments  on  the  production  and  the 
utilization  of  compressed  air  will,  it  is  hoped,  prove  to  the  con- 
trary, and  we  will  try  to  illustrate  the  laws  and  properties 
of  air  and  compressed  air  in  a  simple  manner,  and  with  the 
constant  remembrance  that  practical  men  want  plain  facts  and 
have  no  use  for  mathematical- discussions. 

It  is  a  common  feature  with  gaseous  substances  that  heat 
has  a  tendency  to  increase  their  volume,  or,  as  the  term  goes, 
to  expand  them.  Referring  more  particularly  to  atmospheric 
air,  it  will  suffice  to  recall  the  classical  experiment  of  the  cork 
shutting  hermetically  a  bottle  full  of  air,  and  blown  out,  if  the 
bottle  be  dipped  in  hot  water. 

Therefore^  if  a  certain  amount  of  air  is  confined  within  a 
closed  cylinder,  at  the  outside  temperature,  and  then  exposed  to 
a  source  of  heat,  this  air  will  have  a  tendency  to  expand,  the 
result  of  which  may  be  twofold. 

If  the  cylinder  is  closed,  for  instance,  by  two  covers  tightly 
bolted  on,  and  if  its  walls  and  covers  are  strong  enough  to 
resist  deformation  under  this  expansive  tendency,  the  volume 
of  air  will  remain  constant,  and  its  pressure  will  increase. 

But  if  we  suppose  that  one  of  the  covers  be  removed,  and 
replaced  by  a  tight-fitting  piston  free  to  move  in  the  cylin- 
der, and  loaded  with  a  certain  weight,  when  the  air  is  at  the 
outside  temperature,  the  piston  will  descend  in  the  cylinder 
until  it  is  balanced  by  the  pressure  of  the  confined  cushion  of 
air. 

If  now  the  cylinder  is  heated,  the  piston  will  start  slowly 
upward,  and  then  stop  when  the  expansion  will  have  ceased; 
in  this  case,  the  load  of  the  piston,  and  consequently  the  pres- 
sure of  the  air,  have  remained  the  same  as  before  heating,  but 
the  volume  of  air  has  increased. 

Summing  up  these  simple  facts,  we  will  say,  therefore,  that 
the  effect  of  heat  upon  this  mass  of  air  is,  in  the  first  c?se,  to 
increase  its  pressure  under  constant  volume;  and  in  the  second  case, 
to  increase  its  volume  under  constant  pressure.  The  reverse  would 
happen  in  both  cases;  i.  e.,  if  we  take  the  closed  cylinder  full 
of  hot  air,  and  if  we  allow  it  to  cool  down  to  the  outside  tem- 
perature, the  volume  of  this  air  will,  of  course,  remain  the 
same,  but  its  pressure  will  fall  gradually,  until  it  becomes  the 
same  as  it  was  before  heating. 

In  a  similar  way,  if  we  allow  the  cylinder  with  its  piston  to 
cool  down  to  the  outside  temperature,  the  volume  of  air  con- 
fined under  the  piston  will  shrink,  and  the  piston  will  grad- 
ually drop  down  to  the  point  where  it  was  before  the  cylinder 
was  heated,  the  pressure,  of  course,  remaining  constant. 

Now,    following  this  line  of  reasoning,   we  may  conceive 


6  COMPRESSED    AIR. 

that,  if  the  temperature  around  the  cylinder  was  made  colder 
and  colder,  the  pressure  of  the  constant  volume  of  air  of  the 
first  case  would  keep  dropping,  and  the  volume  of  the  mass  of 
air  at  constant  pressure,  in  the  second  case,  would  also  keep 
shrinking,  until,  if  such  a  process  was  carried  on  far  enough, 
the  mass  of  air  which  we  have  been  considering  would  be  con- 
densed in  volume  to  nothing,  and  have  no  pressure  at  all. 

A  simple  calculation  shows  that  such  a  result  would  occur 
at  the  temperature  of  461  degrees  below  o  Fahr.,  or  493  degrees 
below  the  freezing  point  of  water. 

This  temperature,  which  has  been  approached,  but  never 
yet  reached  by  any  contrivance  at  present  at  our  command,  is, 
so  far,  a  matter  of  mental  conception,  but  we  may,  however, 
conceive  its  existence.  It  is  called  the  absolute  zero,  and  plays 
an  important  part  in  the  study  of  the  properties  of  gases. 

The  absolute  zero  is,  therefore,  the  temperature  at  which  a  mass  of 
air  would  have  neither  volume  nor  pressure. 

Passing  now  to  a  seemingly  different  subject,  although  its 
close  connection  to  the  preceding  facts  will  soon  appear,  a  few 
words  may  be  said  about  the  fundamental  principle  which 
forms  the  basis  of  all  questions  relating  to  the  mechanics  of 
gases,  the  Principle  of  Equivalence  of  Heat  and  Work. 

This  principle,  formulated  in  plain  language,  means  that 
whenever  work  is  performed,  it  develops  heat;  and  conversely,  that 
whenever  heat  is  generated,  it  can  be  tranc "formed  into  work. 

The  scope  of  this  principle  is  exceedingly  broad. 

The  elementary  conception  of  work  involves  two  distinct 
elements:  a  force  and  a  motion,  and  the  measure  of  the 
amount  of  work  developed  by  a  certain  force  is  the  product  of 
this  force,  multiplied  by  its  displacement. 

Thus,  if  we  exert  a  pull  of  i  lb.,  and  if  we  move  i  foot  in 
the  direction  of  this  pull,  the  work  that  we  have  developed 
amounts  to  i-foot  pound. 

But,  while  this  definition  is  true  in  all  cases,  work,  in  nat- 
ural phenomena,  can  assume  a  very  great  variety  of  forms, 
which,  moreover,  it  is  not  necessary  to  enumerate  here. 

Our  daily  experience  shows  us  some  applications  of  this 
principle  of  equivalence,  or  correspondence,  between  heat  and 
work. 

That  work  develops  heat,  we  can  see  in  hammering  a  cold  bar 
of  iron,  which  soon  becomes  hot;  we  see  it  in  the  result  of 
human  exertion,  in  the  heating  of  a  shaft  journal  when  the 
work  of  friction  becomes  too  great;  in  the  sparks  showing  at 
the  contact  of  a  revolving  wheel,  and  of  a  brake-shoe,  or  at  the 
periphery  of  a  grindstone,  etc. 

That  heat  can  b^  transformed  into  work  has  been  shown  in  the 
preceding  explanations,  when  we  saw  a  weighted  piston  lifted 
by  heating  the  air  confined  beneath  it. 

The  steam  engine  is  another  indirect  demonstration  of  the 
same  fact;  when  the  heat  developed  in  the  combustion  of  coal 
generates  steam,  which  accomplishes  some  work  on  the  piston 
of  an  engine. 


COMPRKSSKD   AIR.  7 

It  would  be  useless  to  multiply  examples  of  this  capital 
principle;  suffice  it  to  say,  that  whenever  work  is  performed, 
there  is  a  production  of  heat.  This  will  not  always  be  sensible, 
especially  if  the  work  is  slow  and  gradual,  because  the  heat  is 
lost  by  radiation,  by  absorption  in  surrounding  bodies,  etc.,  as 
soon  as  it  is  developed. 

This  subject  of  the  equivalence  between  heat  and  work  has 
been  exhaustively  studied  and  verified,  and  it  is  now  accepted 
as  a  fundamental  axiom  in  mechanics. 

One  British  Thermal  Unit  (B.  T.  U.)  of  heat,  i.  e.,  the  quan- 
tity of  heat  required  to  raise  by  i  degree  Fahr.  the  tempera- 
ture of  I  It?,  of  water,  corresponds  to  77 8-foot  Ibs.  of  work. 

In  other  words,  778-foot  Ibs.  of  work  applied  to  a  certain 
mass  of  air,  for  instance,  will  develop  in  it  i  B.  T.  U.  of  heat;  and 
conversely,  an  amount  of  heat  of  i  B.  T.  U.  stored  up  in  this 
air  can  develop  778-foot  Ibs.  of  work. 

The  number  778,  or  coefficient  of  correspondence  between 
heat  and  work,  is  known  as  the  Joule's  Equivalent,  from  the 
name  of  the  physicist  who  first  set  precise  rules  in  this  respect. 
Joule  had  fixed  the  figure  at  772-foot  Ibs.,  which  was  for  years 
adopted  as  correct.  Subsequent  investigation  led  to  make  it 
778,  and  the  most  recent  developments  put  it  at  779.  In  this 
treatise  it  has  been  taken  as  778. 

But  it  is  now  expedient  to  clearly  explain  how  a  certain 
mass  of  air,  which  has  been  subjected  to  work,  and  which  has 
therefore  accumulated  a  certain  amount  of  heat,  can  conversely 
develop  work  corresponding  to  that  heat. 

Let  us  take  a  cylinder  full  of  air  at  atmospheric  pressure, 
and  closed  at  one  end,  and  then  let  us  insert  at  the  other  end  a 
piston  in  this  cylinder,  and  exert  an  effort  upon  the  piston; 
the  air  confined  within  the  cylinder  will  be  gradually  com- 
pressed, and  occupy  a  smaller  volume.  At  the  same  time,  its 
pressure  will  have  increased,  and  this  compression  has  absorbed 
a  certain  amount  of  work,  which  will  be  measured  by  the  mean 
pressure  which  the  piston  has  had  to  overcome,  multiplied  by 
the  amount  of  its  displacement.  « 

The  pressure  on  the  piston  represents  a  certain  number  of 
Ibs.;  the  displacement  represents  a  certain  number  of  feet, 
and  their  product  represents  a  certain  number  of  foot-lbs., 
which  measure  the  work  of  compression. 

Suppose  now  that  we  release  the  piston;  the  air  confined  in 
the  cylinder,  and  whose  pressure  was  solely  owing  to  the  effort 
exerted  on  this  piston,  will  immediately  expand  and  push  it 
back,  and  if  there  was  no  friction  between  it  and  the  cylinder 
walls,  it  would  resume  its  former  position,  when  the  air-cushion 
would  be  at  atmospheric  pressure  again.  In  other  words, 
every  amount  of  work  spent  in  compressing  the  air,  would  be 
entirely  returned  by  the  expansion  of  this  air,  or,  to  any  work  of 
cflhipres\ion  corresponds  an  equal  work  of  expansion,  if  these  efforts 
follow  each  other  instantly. 

Here,  we  did  not  make  any  assumption  as  to  the  tempera- 
ture of  the  confined  air,  which  has  been  supposed  to  remain 


3  COMPRESSED   AIR. 

stationary.  But  now  let  us  confine,  with  a  piston,  a  certain 
amount  of  free  air  in  a  cylinder,  and  let  us  fix  the  piston  in 
this  position  so  as  to  prevent  it  from  backing  out;  and,  then,  let 
us  apply  to  the  cylinder  some  source  of  heat. 

The  confined  air  will  have  a  tendency  to  expand,  and  as  the 
piston  cannot  move,  the  pressure  will  rise;  if  then  we  let  the 
piston  free,  the  confined  air  will  push  it  out  in  expanding, 
until  it  resumes  the  atmospheric  pressure,  and  the  outside  tem- 
perature, and  with  the  same  restriction  as  regards  frictional 
resistances. 

We  see  that  in  both  instances  there  has  been  some  expan- 
sive work  done,  and  the  force  that  produced  it  was  supplied  in 
the  first  case  by  the  work  of  compression,  and  in  the  second 
case,  by  the  heating  of  the  air.  We  see  also  that  in  this  latter- 
instance,  the  pressure  of  air  in  the  cylinder  depended  upon  the 
amount  of  heat  supplied  to  it,  or,  in  other  words,  upon  its  tem- 
perature, and  so  did  the  expansion  work. 

Returning  now  to  the  definition  of  the  absolute  zero,  as 
given,  which  marks,  so  to  say,  the  ideal  limit  of  existence  of  a 
gas  so  far  as  volume  and  pressure  are  concerned,  we  can 
readily  conceive  that  i  Ib.  of  atmospheric  air,  at  60  degrees 
Fahr.,  for  instance,  is  the  outcome  of  i  Ib.  of  air  at  the  tempera- 
ture of  absolute  zero,  to  which  a  sufficient  amount  of  heat  has 
been  supplied  to  raise  its  temperature  by  461  +60=521  degrees 
Fahr.,  and  its  pressure  to  14.7  Ibs.  per  square  inch,  above  a 
vacuum,  which  is  the  pressure  at  the  absolute  zero. 

This  pound  of  air  is  confined  within  the  atmosphere,  as  was 
the  mass  of  air  of  the  last  example  within  a  cylinder;  but 
should  it  be  allowed  to  expand  against  a  perfect  vacuum,  it 
would  produce  an  amount  of  expansion  work  corresponding  to 
.  the  amount  of  heat  which  it  had  received  to  become  atmos- 
pheric air. 

This  capacity  of  producing  expansion  work  is  what  is 
termed  the  Intrinsic  energy  of  this  pound  of  air,  and  its  exist- 
ence is,  as  we  see,  intimately  connected  with  the  conception  of 
the  absolute  zero.  * 

The  amount  of  work  that  measures  this  intrinsic  energy  can 
be  determined  from  the  law  of  the  equivalence  of  heat  and 
work,  since  we  know  that  by  storing  up  a  certain  quantity  of 
heat  in  a  mass  of  air,  we  give  it  the  property  of  returning  a 
corresponding  quantity  of  work. 

The  temperature  to  which  a  given  amount  of  heat  will  raise 
i  Ib.  of  different  substances  is  not  the  same  for  all  of  them. 

The  specific  heat  of  a  substance  is  the  number  of  B.  T.  U. 
that  will  raise  by  i  degree  Fahr.  the  temperature  of  i  Ib. 
of  this  substance,  the  specific  heat  of  water  being  taken  as 
unit.  We  have  seen  already  that  the  specific  heat  of  water  was  i ; 
i.  e.,  that  it  takes  i  B.  T.  U.  to  raise  by  i  degree  Fahrenheit  the 
temperature  of  i  Ib.  of  water. 

The  specific  heat  of  air  which  we  have  to  use  in  the  subse- 
quent developments  is  0.2377. 

In  other  words,  it  takes  0.2377  of  a  B.  T.  U.  to  raise  by  i 


COMPRESSED  ATTR^CAUFC 

_-. — • *" 

degree  the  temperature  of  I  Ib.  of  air,  that  is  to  say,  the 
amount  of  heat  that  would  raise  by  i  degree  Fahr.  the  tem- 
perature of  i  Ib.  of  water,  will  raise  by  i  degree  Fahr.  the 
temperature  of  4.2  Ibs.  of  air. 

The  quantity  of  heat  necessary  to  raise  by  521  degrees  Fahr. 
the  temperature  of  i  Ib.  of  air  is,  therefore: 

0.2377X521=123.8412  B.  T.  U., 
and  the  corresponding  amount  of  work  is, 

123.8412x778=96,348.52  foot  Ibs., 

which  represents  the  Intrinsic  energy  of  i  Ib.  of  air  at  60  de 
grees  Fahr. 

This,  of  course,  presumes  that  no  heat  would  be  either  lost 
or  gained,  by  radiation  or  otherwise,  during  the  expansion  of 
air,  and  this  sort  of  expansion  is  called  Adiabatic  expansion. 

Now,  while  any  one  will  readily  understand  that  the  expan- 
sion of  air  can  be  utilized  to  do  useful  work  on  a  piston,  it  is 
also  obvious,  for  practical  reasons,  that  this  expansion  cannot 
be  carried  below  atmospheric  pressure,  since  creating  a  vacuum 
would  require  additional  work. 

Consequently,  we  cannot  expect  to  avail  ourselves  of  any 
portion  of  the  intrinsic  energy  stored  up  in  atmospheric  air, 
under  ordinary  circumstances. 

With  a  steam  engine  we  can  obtain  a  vacuum,  or  at  least  a 
pressure  inferior  to  the  atmosphere,  by  condensing  the  steam, 
but  there  is  no  such  thing  in  the  air  machine. 

Let  us  observe,  moreover,  that  the  intrinsic  energy  pos- 
sessed by  i  Ib.  of  air  is  entirely  independent  of  its  pressure,  so 
long  as  its  temperature  remains  the  same,  the  work  of  expan- 
sion being  exclusively  controlled  by  the  extreme  temperatures 
between  which  the  air  expands;  so  that  i  Ib.  of  air  at  100  Ibs. 
gauge  pressure,  and  I  Ib.  of  air  at  10  Ibs.  gauge  pressure,  and 
both  at  60  degrees  Fahr.,  possess  the  same  total  intrinsic 
energy  as  i  Ib.  of  atmospheric  air. 

But  there  is  a  vast  difference  between  them  at  a  practical 
standpoint,  inasmuch  as  air  at  100  Ibs.,  and  even  at  TO  Ibs. ,  can 
do  some  useful  work  by  expanding  down  to  atmospheric  pres- 
sure; part  of  their  intrinsic  energy  can,  therefore,  be  utilized  to 
do  some  actual  work. 

Taking,  for  instance,  i  Ib.  of  air  at  100  Ibs.  gauge,  and  at  60 
degrees  Fahr. — if  allowed  to  expand  adiabatically  to  atmos- 
pheric pressure,  it  will  produce  work,  and  consequently  lose 
part  of  its  heat,  and  we  find  that  its  temperature,  after  the 
expansion  has  taken  place,  is: —  173.95  degrees  Fahr. 

The  drop  of  temperature  is: 

i73-95+6o= 233  95  degrees. 

and  as  778 yso. 2377=184  93,  the  work  of  adiabatic  expansion  is: 
184.93x233-95=  43,264.37  ft.  Ibs. 

this  being  the  useful  work, 

The  adiabatic  work  of  expansion  from  173. 9S 
degrees  Fahrenheit  to  the  absolute  o  would 
be:  18493x287.05=  53,084.15  ' 

Total,  96,348.52     "      ' 


COMPRESSED   AIR. 


COMPRESSED    AIR.  II 

which   is  the  total   intrinsic  energy — that  is  to  say,  we  have 
utilized  45  per  cent  of  the  total  intrinsic  energy. 

Next,  taking  air  at  10  Ibs.  gauge,  the  temperature  after  adia- 
batic  expansion  to  atmospheric  pressure  is —  12.9  degrees  Fahr. , 
and  the  useful  work  of  expansion  is: 

184.93x72 .9=  i3.48i.39   ft-    Ibs. 

The  adiabatic  expansion  from  —  12.9  degrees 
to  absolute  zero  would  give: 

184.93X448.1=  82,867.13    ' 

Total,  96,348.52    "    '" 
i.  e.,  the  total  intrinsic  energy,  and  the  useful  work  is  here  14 
per  cent  of  the  total  intrinsic  energy. 

It  is  hardly,  necessary  to  say  that  these  figures  are  theoreti- 
cal, because,  in  practise,  part  of  the  work  of  expansion,  and 
consequently  part  of  the  heat,  is  absorbed  by  the  friction  of 
the  piston  in  the  cylinder,  and  lost  by  radiation  from  the  vari- 
ous pieces  of  the  machines. 

We  see,  therefore,  that  the  only  portion  of  the  intrinsic 
energy  of  air  that  is  practically  obtainable  is  the  expansion 
work  which  it  does  above  atmospheric  pressure;  i.  e.,  that  the 
pressure  of  this  air  must  be  raised  above  the  pressure  of  the 
atmosphere. 

From  the  preceding  developments  we  might  rightly  con- 
clude that  this  result  would  be  reached  by  heating  the  air, 
previously  confined  within  a  closed  vessel,  to  a  proper  temper- 
ature. But  in  practise,  such  a  process  would  prove  unaccept- 
able. 

Compressed  air  is  slow  in  taking  up  heat,  because  its  con- 
ductivity is  small ;  i.e.,  because  the  heat  is  slow  to  penetrate  the 
whole  mass  of  air,  and  its  low  specific  heat  causes  it  to  cool 
down  rapidly. 

Then,  again,  the  whole  amount  of  expansive  work  above 
atmospheric  pressure  could  not,  as  said  before,  be  obtained  in 
practise;  so  that  raising  the  pressure  of  air  by  mere  heating  is 
not  a  practical  proposition,  and  it  is  necessary,  in  order  to 
meet  the  requirements  of  its  industrial  applications,  to  operate 
this  rise  of  pressure  by  direct  compression;  i.  e.,  by  acting  upon 
the  air,  confined  in  a  cylinder,  through  a  piston  to  which  an 
adequate  amount  of  power  is  applied. 

This  compression,  in  whichever  way  the  rise  of  pressure 
occurs  during  its  process,  is  always  aff-cted  on  the  following 
general  lines: 

A  cylinder  A  (Fig.  i),  closed  at  both  ends  by  covers,  con- 
tains a  piston  B,  which  can  move  back  and  forth  therein,  and 
whose  rod  C  is  connected,  either  to  the  piston  of  a  steam 
engine,  or,  through  a  connecting-rod  and  a  crank,  to  a  revolv- 
ing shaft. 

Each  one  of  the  cylinder  covers  carries  one  or  more  inlet 
valves  «,  af ',  through  which  the  atmospheric  air  can  penetrate 
into  the  cylinder;  each  valve,  of  course,  opening  inward,  and 
being  maintained  tightly  pressed  upon  its  seat  by  a  spring. 


12  COMPRESSED   AIR. 

The  covers  also  carry  one  or  more  discharge  valves  C  C't 
similarly  kept  closed  by  a  spring,  and  opening  outward  into 
closed  chambers  g,  h,  connected  by  a  common  conduit  c, 
which  leads  to  a  closed  receiver  r,  whence  a  pipe  attached  to 
the  nozzle  s,  conveys  the  air  to  the  place  where  it  is  proposed 
to  use  it. 

All  the  valves  being  closed,  and  the  piston  />*  at  one  end  of 
its  stroke,  as  shown,  if  it  is  set  in  motion  from  the  left  to  the 
right,  a  partial  and  increasing  fall  of  air  pressure  will  occur 
behind  it,  and  soon  overcome  the  tension  of  the  spring  which 
keeps  the  inlet  valve  a  closed;  this  valve  opens,  and  atmos- 
pheric air  rushes  into  the  cylinder,  behind  the  receding  piston. 

On  the  right  side  of  this  latter,  we  have,  at  the  beginning  of 
the  stroke,  a  cylinder  full  of  atmospheric,  or,  as  generally 
called,  of  free  air;  the  inlet  valve  a,  and  discharge  valve  /',  are 
both  closed,  and  so  remain  as  the  piston  moves  from  left  to 
right,  because  the  air  pressure  in  the  cylinder  has  a  tendency 
to  close  the  inlet  valve  «',  whilst  its  pressure  is  not  sufficient  to 
lift  the  discharge  valve  b> '. 

The  piston  continuing  to  move,  the  air  pressure  constantly 
increases,  until,  at  a  certain  point  ;/  of  the  stroke  it  reaches,  or 
slightly  surpasses,  the  receiver  pressure. 

The  action  of  this  latter  on  the  outerside  of  the  discharge 
valve  £',  and  also  the  tension  of  its  spring  are  now  balanced, 
and  the  smallest  subsequent  move  of  the  piston  opens  this 
valve,  and  the  compressed  air  is  forced  through  it  into  the 
receiver,  until  the  piston  reaches  the  end  of  its  stroke,  when 
the  discharge  valve  is  closed  by  its  spring. 

An  inverse  series  of  operations  will  occur  during  the  reverse 
stroke,  and  so  on. 

An  analysis  of  these  operations  shows  that  during  any  one 
stroke  of  the  piston  there  are  three  distinct  classes  of  work  per- 
formed: on  one  side  of  the  piston,  a  work  of  suction;  on  the 
other  side,  first  a  work  of  compression,  under  variable  piston 
load,  and  then  a  work  of  delivery,  under  constant  piston  load. 

This  is  quite  similar,  only  in  the  reverse  order,  to  what 
occurs  in  the  cylinder  of  a  steam  engine,  wherein  a  certain 
volume  of  steam  is  admitted  under  full  pressure,  and  then, 
after  cutting  off  its  ingress,  is  allowed  to  expand  during  the 
remainder  of  the  stroke. 

The  work  of  suction,  which  overcomes  the  inertia  of  the  in- 
let valves,  the  tension  of  their  springs,  and  the  resistance  of 
air  in  its  passage  through  the  valve  apertures,  is  always  small, 
and  can  be  reduced  by  properly  proportioning  and  constructing 
the  inlet  valves. 

It  is,  therefore,  a  matter  of  correct  design,  which  has  nothing 
to  do  in  the  present  developments,  and  no  further  mention  of 
it  will  hereafter  be  made. 

Of  the  two  other  qualities  of  work,  the  peiiod  of  delivery 
does  not  either  offer  any  peculiar  feature  to  investigation 
besides  its  relative  proportion  to  the  whole  stroke,  inasmuch  as 
it  is  symbolized  by  a  constant  load  acting  against  the  piston, 


COMPRKSSED    AIR.  13 

along  a  certain  distance,  which  corresponds  to  the  elementary 
definition  of  work  as  previously  given. 

We  are  thus  left  to  concentrate  our  attention  upon  the 
period  of  compression. 

The  variations  of  volume  and  of  pressure  of  air,  which  occur 
gradually  during  the  process  of  compression,  do  not  follow  the 
same  law  in  all  cases;  that  is  to  say,  this  variation  is  different, 
whether  the  compression  takes  place  at  a  constant  temperature 
(isothermal  compression)  without  any  loss  or  gain  of  heat,  or 
by  allowing  the  increasing  heat  developed  during  the  com- 
pression to  remain  integrally  in  the  air;  in  other  words,  if  the 
compression  is  done  at  variable  temperature  (adiabatic  com- 
pression). 

There  is  no  intention  to  develop  here  the  laws  governing 
the  pressure  and  volume  of  air  in  those  two  sorts  of  compression. 

This  would  necessarily  involve  the  use  of  mathematical 
formulae,  which  we  wish  to  avoid.  Suffice  it  to  say  that,  if  the 
temperature  of  the  air  remained  constant  throughout  the  compression , 
the  volume  which  it  occupies  at  any  moment  would  vary  in- 
versely as  the  pressure. 

Taking,  for  instance,  i  cubic  foot  of  free  air  at  60  degrees 
Fahr.,  its  pressure  is,  therefore,  i  atmosphere,  or  14.7  Ibs.  per 
square  inch  above  a  vacuum,  or  also  zero  gauge  pressure. 
Suppose  that  this  air  is  confined  under  the  piston  of  a 
closed  cylinder,  and  that,  driving  this  piston  forward,  we 
reduce  the  volume  occupied  by  the  air  to  }4  cubic  foot  only,  at 
the  same  time  maintaining  always  its  temperature  at  60  degrees 
Fahr.  Then  the  pressure  of  this  air  would  be  29.4  Ibs.  per 
square  inch  above  a  vacuum  (or  14.7  Ibs.  gauge),  that  is,  twice 
what  it  was  before. 

If  the  volume  was  reduced  to  ^  of  a  cubic  foot,  its  pressure 
would  become  3x14.7,  or  44.1  Ibs.  per  square  inch  above  a 
vacuum  or  29.4  Ibs.  gauge,  always  upon  the  condition  that  the 
temperature  remains,  throughout  this  process,  at  60  degrees 
Fahr. 

In  other  words,  if  the  volume  of  air  becomes  4,  5,  6,  10,  20 
times  smaller,  its  pressure  becomes  4,  5,  6,  10,  20  times  greater, 
always  taking  the  pressure  of  the  atmosphere  (or  the  gauge  pressure 
plus  14  7  Ibs.  per  square  inch)  as  unit,  and  not  the  gauge  pres- 
sure, which  would  lead  to  absurd  conclusions. 

These  pressures  counted  above  a  vacuum  are  called  absolute 
pressures;  the  pressures  indicated  by  the  pressure  gauge  of  a 
boiler  are  termed  effective  or  gauge  pressures.  The  absolute  pres- 
sure is  obtained  by  adding  14.7  Ibs.  to  the  corresponding  gauge 
pressure;  and  conversely,  the  gauge  pressure  is  obtained  by 
subtracting  14.7  Ibs.  from  the  corresponding  absolute  pressure. 

Let  us  take  a  cylinder  open  at  one  end  (Fig.  2)  and  a  piston 
moving  in  it.  Suppose  that  the  piston  is  at  48  inches  from  the 
cylinder  head,  that  this  space  has  been  filled  with  free  air 
through  the  inlet  valve,  and  that  the  pipe  leading  from  the 
discharge  valve  casing  communicates  with  a  receiver  wherein 
the  pressure  is  73.5  Ibs.  gauge  per  square  inch.  ^* 

j^         **  ncTur 


COMPRESSED   AIR. 


COMPRESSED   AIR.  15 

We  will  assume,  also,  that  the  compression  is  isothermal; 
i.  e.,  that  the  temperature  in  the  interior  of  the  cylinder  re- 
mains the  same  as  in  the  open  air. 

If  we  move  the  piston  12  inches,  the  volume  occupied  by 
the  air  is  36  inches,  or  #  of  its  former  length,  4^  inches.     The 
pressure  must,  therefore,  be  the  reverse,  or  %  of  the  atmos- 
•pheric  pressure;  i.  e.,  19.6  Ibs.  absolute,  or  4.9  Ibs  gauge. 

Similarly,  when  the  piston  has  successively  covered 
24>       32»       36»  38.4    46  inches  of  its  stroke,  the  absolute 

pressures  are  respectively: 

29.4,   44.1,    58.8,        73.5,    82.2  Ibs.,  and  the  gauge  pressures 
14.7,    29.4,   44.1,       58.8,    73  5  Ibs.,  per  square  inch, 
which  are  marked  on  the  sketch. 

If  the  piston  moves  further  on,  as  the  pressure  in  the  cylin- 
der is  the  same  as  in  the  receiver,  the  discharge  valve  opens; 
there  is  no  more  compression,  and  the  remaining  8  inches  of 
stroke  are  completed  by  the  piston  against  a  constant  gauge 
pressure  of  73.5  Ibs.  per  square  inch. 

Let  us  now  draw  a  line,  A  D,  which,  at  any  scale,  repre- 
sents 48  inches,  and  mark  on  this  line  some  points  at  12,  24,  32,. 
36,  38.4,  and  40  inches  from  its  left  end;  then  draw  at  those 
points  some  lines  12-2,  24-3,  32-4,  36-5,  38  4-6,  40-7,  perpendic- 
ular to  A  D. 

Now,  on  these  lines,  let  us  carry,  at  any  other  scale,  the 
gauge  pressure  at  the  corresponding"  point  of  the  stroke;  this 
will  give  us  a  succession  of  points  2-3-4-5-6-7,  and,  if  we  join 
them  by  a  continuous  line,  a  curve  A  B,  that  represents  the 
variations  of  air  pressure  during  the  compression. 

This  curve  starts  from  the  point  A,  where  the  gauge  pres- 
sure is  zero. 

If  we  took  any  number  of  inter-mediate  points  between  40- 
and  48  inches  of  the  stroke,  the  pressure  would  always  be  73.5 
Ibs.  gauge,  and  consequently  the  curve  of  compression  A  B  is 
followed  by  a  line  B  L\  parallel  to  A  D,  and  representing  the 
delivery  under  constant  pressure:  so  the  diagram  A  B  CD  gives^ 
us  a  graphic  representation  of  the  isothermal  compression  and 
delivery  of  air  during  one  stroke  of  the  piston,  and  its  area 
represents  the  work  performed  during'  that  stroke,  for  each 
square  inch  of  piston  area. 

The  law  of  isothermal  variation  of  the  pressures  and  vol- 
umes applies  to  decreasing  pressures  as  well  as  to  increasing 
ones;  thus,  if  we  cause  one  cubic  foot  of  air  at  73.5  Ibs.  gauge 
(88,2  absolute)  to  occupy  6  cubic  feet,  its  pressure  will  become 
14.7  Ibs.  absolute  per  square  inch  or  o  gauge  pressure. 

In  other  words,  the  curve  of  isothermal  compression  is  also 
the  curve  of  isothermal  expansion,  and  the  diagram  ABC  D 
represents  either  the  work  of  compression  and  delivery  of  a 
volume  of  free  air,  to  73.5  Ibs.  gauge,  or  the  expansive  work  of 
the  same  body  of  air  at  73.5  Ibs,  gauge  pressure,  and  expanded 
from  that  pressure  to  the  atmosphere,  when  it  resumes  its  prim- 
itive volume. 

The  practical  meaning  of  this  is,   that  if  we  compress  a 


I  6  COMPRESSED   AIR. 

certain  mass  of  air  in  a  closed  cylinder,  by  pushing  the  piston 
forward  by  a  certain  number  of  inches,  and  then,  if  we  let  the 
piston  free,  the  air  will  expand  and  push  it  back;  and  should 
there  be  no  friction  between  the  cylinder  and  the  piston,  this 
latter  would  return  exactly  to  its  starting-point,  performing 
during  its  reverse  stroke  exactly  as  much  work  as  has  been 
required  to  push  it  forward. 

Quite  a  similar  course  of  reasoning  leads  us  to  conclude  that 
if  we  compress  air  isotherinally  in  a  cylinder,  and  if  its  discharge 
valve  chamber  (this  valve  being  loaded  to  receive  pressure) 
communicates  through  a  pipe  of  any  length,  with  another 
cylinder  exactly  alike,  located  at  some  distance  from  the  com- 
pressing cylinder,  we  can  obtain  isothermally  (neglecting 
resistances)  from  the  second  cylinder  the  same  amount  of 
work  that  has  been  developed  in  the  distant  first  cylinder. 
The  first  cylinder  is  the  compressor,  'the  second  is  the  motor, 
connected  by  the  air  main  to  the  compressor;  the  whole  is  a 
perfect  compressed  air  transmission,  wherein  a  given  amount  of 
work  is  integrally  conveyed  to  any  distance  from  its  point  of 
production. 

But  were  we  to  establish  such  a  system  we  would  find  that 
in  practise  the  work  recovered  from  the  motor  would  not  be 
equal  to  the  work  developed  in  the  compressor. 

To  reduce  this  difference  (which  is  the  keynote  of  economy 
in  this  system  of  power  transmission)  to  be  as  small  as 
possible,  constitutes,  in  a  nutshell,  the  whole  scope  of  pneu- 
matic engineering;  and  as  the  first  condition  to  fight  a 
difficulty  is  to  locate  it,  and  to  size  it  up,  these  remarks  will  be 
concluded  by  a  few  explanations  showing  what  are  the  causes 
of  discrepancy  between  the  work  expended  in  the  compressor, 
and  the  work  recovered  from  the  motor,  and  how  they  can  be 
partly  eliminated;  their  total  disappearance,  or  rather  counter- 
acting, being  a  purely  practical  matter,  which  has  no  absolute 
limitations. 

The  fact  of  compressing  air  in  a  cylinder  is  always  accom- 
panied by  a  production  of  heat.  What  causes  this  heat  to 
develop  in  the  case  of  air  is  a  question  the  precise  answer  to 
which  would  carry  us  too  far  into  theory.  It  may  be  said 
however,  that  modern  science  considers  air  as  formed  of 
minute  particles  in  a  constant  state  of  vibration,  and  that  com- 
pressing a  volume  of  air  which  contains  a  certain  number  of 
these  particles  causes  them  to  increase  the  rapidity  of  their 
vibratory  motions,  hence  friction,  impact,  and  heat. 

Direct  experiment,  made  from  the  freezing  to  the  boiling 
point  of  water,  has  shown  that  the  pressure  of  air  remaining 
the  same,  its  volume  at  32  degrees  Fahr.  increases  by  /^93  for 
each  increase  of  i  degree  Fahr.  in  the  temperature  of  this  air. 

From  this  we  see  that  air  at  the  temperature  of  boiling 
water  has  increased  in  volume  by  I8%93— 0.366,  or  36.6  per 
cent,  whilst  this  same  air,  at  493  degrees  below  the  freezing 
point  of  water,  or  461  degrees  below  zero  Fahr.  has  shrunken 
by  49Xga  of  its  volume,  or  by  that  volume  itself.  This  is  how 
;the  temperature  of  absolute  zero  was  ascertained. 


COMPRESSED   AIR.  17 

Compression  will  generate  heat,  and  only  should  it  be  pos- 
sible to  eliminate  it  as  soon  as  produced,  would  isothermal 
compression  be  obtainable.  It  might  probably  be  done  by  a 
very  slow  and  gradual  compression,  combined  with  copious 
means  of  cooling  the  air  in  the  compressing  cylinder. 

But  these  conditions  correspond  to  a  practical  impossibility, 
and  there  is  in  consequence  a  considerable  amount  of  heat  dis- 
engaged during  the  compression.  The  following  table  gives 
the  temperatures  Fahr.  of  dry  air  at  the  end  of  its  compression, 
to  different  gauge  pressures  in  adiabatic  compression;  i.  e., 
supposing  that  no  portion  of  the  heat  developing  is  lost  in  the 
course  of  compression. 

Absolute  Pressure.  Gauge  Pressure.  Fahr.  temperature  at 

(Lbs.  per  sq.  in.)  (I^bs.  per  sq.  in.)  end  of  compression. 

14.7  o  60° 

16.17                                        1.47  74-6° 

18.37                                 3-67  94-8° 

22.05                                 7-35  124.9° 

25.81  ii. II  151.6° 

29.4  14.7  175-8° 

36.7  22  218.3° 
44-1                   29.4                  255.I0 
51-4                   36.7  287.8° 

58.8  44-1  3I740 
73-5                                    58.8  369.4° 
£8.2                                73.5                                414-5° 

102.9  88-2  454-5° 

117.6  102.9  490.6° 

132.3  117.6  523  7° 

M7  132.3  554° 

220.5  205-8  .      681° 

294  279.3  781° 

367.5  352.8  864° 

We  see  that  as  the  pressure  increases  so  does  the  tem- 
perature, and  that  when,  for  instance,  the  pressure  has  reached 
73.5  Ibs.  gauge  per  square  inch,  the  temperature  is  414.5 
degrees  Fahr.,  instead  of  60  degrees,  as  was  the  case  .in 
isothermal  compression. 

The  result  is,  that  if  we  take  the  same  cylinder  which  was 
used  in  that  case,  i.  e.,  if  we  act  on  the  same  weight  of  free  air, 
this  air,  when  at  73.5  Ibs.  gauge,  will  be  354.5  degrees  Fahr. 
warmer  in  adiabatic  compression  than  it  would  in  isothermal 
compression.  Its  volume  must  therefore  be  necessarily  greater 
in  the  former  case,  since  the  pressure  is  supposed  to  be  the  same. 
The  practical  meaning  of  it  is  that  in  adiabatic  work  the 
period  of  compression  is  shorter  and  the  period  of  delivery  is- 
longer  than  in  isothermal  work;  as  the  work  at  full  pressure  is- 
naturally  greater  than  at  anytime  during  compression,  when 
the  pressure  is  smaller,  the  adiabatic  work  is  greater  than  the 
isothermal  work,  to  raise  the  same  weight  of  air  to  the  same 
pressure. 

For   73.5  Ibs.  gauge,  and  atmosphere  at  60  degrees  Fahr., 


IS  COMPRESSED    AIR. 

the  adiabatic  work  is  1.31  times  the  isothermal  work.  But  if 
the  work  done  by  the  motor  is  correspondingly  greater,  what 
harm  does  the  heat  do  ?  There  would  be  none  but  for  the  fact 
that  the  motor  is  always  at  some  distance  from  the  compressor 
(otherwise  there  would  be  no  reason  to  transmit  power),  and 
the  air  parting  easily  with  its  heat,  its  passage  through  the 
receiver  and  the  main  will  reduce  the  air  to  the  temperature  of 
the  atmosphere;  i.  e.,  after  compressing  a  volume  of  hot  air 
F  C  D  G  (Fig.  3),  we  shall  introduce  in  the  motor  a  volume 
B  C  D  E  of  cold  air  of  the  same  weight  and  pressure. 

Now,  this  volume  will  expand  in  the  motor  either  isother- 
mally  or  adiabatically. 

As  we  saw  that  the  work  of  compression  disengages  heat, 
similarly,  but  conversely,  does  the  work  of  expansion  absorb 
heat  from  the  surrounding  bodies,  and  as  the  isothermal  com- 
pression would  require  a  slow  process  with  copious  cooling,  so 
would  the  isothermal  expansion  require  a  slow  process  with 
copious  heating.  Unless  this  is  done,  the  expansion  will  be 
rather  adiabatic. 

Rather,  because  if  isothermal  conditions  never  strictly 
obtain  in  practise,  the  same  is  true  with  adiabatic  work. 

If  we  expand  adiabaticaily  the  volume  of  air  B  C  D  E,  at 
60  degrees  Fahr.  and  73.5  gauge,  to  atmospheric  pressure,  the 
work  of  expansion  represented  by  the  diagram  B  CD  K,  will 
only  be  0.595  of  the  work  of  adiabatic  compression. 

A  compressed  air  transmission  seems,  therefore,  to  be  an 
inferior  system,  the  more  so  as  the  above  figures  do  not  take 
into  account  all  the  losses  incurred,  but  only  the  thermic 
losses;  i.  e.,  such  as  are  due  to  loss  of  heat. 

Several  means  are  resorted  to  in  order  to  reduce  this  loss. 

Suppose  that  the  volume  of  cold  air,  B  C  D  E,  when  it 
arrives  at  the  motor,  be  reheated  at  constant  pressure  (73.5 
Ibs.  g. )  until  it  becomes  equal  to  F  C  D  G;  then  we  shall  be 
able  to  develop  in  the  motor  by  the  expansion  of  this  volume 
of  hot  air  the  same  work  that  was  used  to  compress  it 
adiabatically. 

So  if  there  was  no  other  loss,  the  motor  would  utilize  rooper 
cent  of  the  work  of  compression.  Indeed,  should  the  air  arriv- 
ing at  the  motor  be  reheated  to  a  higher  temperature  than  that 
reached  in  the  compressor,  the  work  recovered  would  be 
greater  than  the  work  expended;  and  there  is  no  absurdity  in 
this  statement,  for  such  a  result  is  easily  attained  at  the  cost  of 
a  certain  quantity  of  fuel,  which  must  be  taken  into  account 
and  deducted  in  figuring  up  the  actual  efficiency  of  the  motor. 

Reheating  the  air  upon  its  arrival  at  the  motor  is,  indeed, 
the  bise  of  the  superiority  of  compressed  air  as  a  medium  of 
power  transmission. 

No  corresponding  feature  exists  with  electricity  to  the  pos- 
sibility of  increasing  at  any  time  the  intrinsic  energy  of  the 
motive  agency  in  an  easy  and  inexpensive  manner. 

There  are,  however— at  least  at  present — some  practical 
limitations  to  this  reheating;  compressed  air  cannot  conve- 


COMPRESSED   AIR. 


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20  COMPRESSED   AIR. 

niently  be  admitted  into  a  cylinder  at  a  temperature  much  above 
350  degrees  F^ahr. ;  while  we  have  seen  that  in  adiabatic  com- 
pression, the  temperature  corresponding  to  73.5  Ibs.  gauge  is 
414.5  degrees,  and  this  illustration  points  out  one  reason  why 
low  pressure  air  is  more  economical,  for  power  purposes,  and  also 
the  use  of  compound  compression  where  the  rise  of  adiabatic 
temperature  is  small  in  comparison  to  single  stage  machines. 

No  lubricants  of  the  ordinary  description  will  be  fully  active 
beyond  this  temperature:  special  oils,  however,  are  made 
which  are  not  decomposed  belore  500  to  6co  Fahr  But  it  is 
evident  that,  could  the  compressor  and  motor  cylinders,  pis- 
tons, and  packings  be  made  of  a  substance  that  would  with- 
stand great  heat  without  injury  or  the  usual  lubricants,  the 
reheating  could  be  carried  far  enough  to  compensate  for  all 
other  losses,  a  feature  exclusively  characteristic  of  air;  and 
there  is  no  apparent  reason  why  such  a  substance  could  not  be 
discovered,  and  it  will  reward  undoubtedly  its  discoverer  in  a 
day  not  far  distant. 

Without  entering  into  many  particulars,  it  may  be  stated 
that  when  the  compression  from  atmospheric  to  receiver  pres- 
sure is  effected  in  one  cylinder,  the  air  is  cooled  either  by  sur- 
rounding the  walls  of  the  cylinder  with  a  jacket,  and  providing 
in  the  heads  some  hollow  chambers,  through  which  a  continu- 
ous stream  of  cold  water  is  rapidly  circulated:  this  is  called 
"  dry  cooling,"  because  no  water  comes  in  contact  with  the 
air,  and  represents,  without  exception,  the  best  American 
practise. 

Or  else,  a  spray  of  finely  divided  cold  water  is  injected  in 
the  body  of  air  under  compression. 

Here,  the  contact  is  direct  between  air  and  water,  so  this 
system  is  more  effective  than  the  dry  cooling;  and  if  the  jacket 
arrangement  is  used  in  connection  with  the  spray,  a  marked 
improvement  occurs  in  the  cooling  of  air. 

This  wet  cooling  has,  however,  some  practical  disadvantages, 
which  led  to  discarding  it  in  this  country,  while  in  Burope  i, 
is  still  found  in  recent  high-class  compressing  plants. 

Another  effective  means  of  cooling  consists  in  compounding 
the  compressor;  i.  e.,  in  effecting  the  total  compression  through 
a  series  of  successive  cylinders,  in  each  one  of  which  only  a 
partial  compression  is  effected,  generating  little  heat,  which  is 
more  easily  dealt  with;  besides,  the  air  in  passing  from  a  cylin- 
der to  the  next  one  in  the  series  is  discharged  through  a 
cooler,  where  it  resumes  the  outside  temperature. 

For  high  pressures,  compounding  is  a  necessity,  and  the 
efficiency  of  the  compression  is  thereby  increased. 

The  ideal  compression  is,  of  course,  the  isothermal;  and  its 
efficiency  being  i,  we  have  the  following  relative  efficiencies 
for  other  systems,  when  air  is  compressed  to  6  atm.  effective, 
namely, 

Adiabatic,  without  cooling 0.744 

Adiabatic,  with  jackets .80 

Adiabatic  with  spray 0.85 


COMPRESSED  AIR.  21 

Adiabatic  compound   (2-stage),   jacketed,    with 

intercooler  but  no  spray 0.863 

3-Stage   compound,   with  intercoolers  and  with 

spray 0.955 

The  effect  of  cooling  is  first  to  improve  the  efficiency  of  the 
compression;  i.  e.,  to  use  less  work  in  producing  it;  and  then, 
at  the  same  time,  the  amount  of  heating  is  proportionally 
reduced. 

A  mere  mention  will  be  made  of  the  loss  incurred  by  the 
air  pressure  on  its  passage  through  the  main  connecting  the 
compressor  and  the  motor. 

Tables  will  be  found  in  this  book  giving  the  loss  of  pressure 
through  mains  of  different  lengths  and  sizes,  and  for  different 
velocities  of  circulation  of  air. 

In  a  general  way,  and  especially  in  a  long  transmission, 
there  is  a  conflict  between  the  first  cost  of  the  plant  and  its 
efficiency,  which  both  increase  with  the  size  of  the  main. 

In  a  properly  built  line,  the  loss  can  be  made  very  small, 
and  its  value  will  generally  be  assumed  to  suit  local  conve- 
nience, according  to  whether  the  first  outlay  or  the  cost  of  power 
is  to  have  more  weight  in  arriving  at  a  decision. 

It  is  hoped  that  the  preceding  remarks  will  enable  any  in- 
telligent reader  to  form  a  correct  idea  of  the  elements  to  be 
taken  into  consideration  in  installing  a  compressed  air  plant  or 
compressed  air  transmission,  and  briefly  they  may  be  enu- 
merated : 

1.  An  economical  prime  motor. 

2.  A  compressor,  which,  while  having  a  high  mechanical 
efficiency,  has  also  means  for  reducing  the  heat  of  compression 
to  a  minimum  during  and  between  the  periods  of  compression. 

3.  A  pipe  line  involving  the  least  loss  by  friction  consist- 
ent with  the  finances  at  command. 

4.  Motors,   which,  beside  possessing  a  high   mechanical 
efficiency,  have  means  to  expand  the  air  to  the  atmospheric 
pressure,  which  must  be  done  by  reheating  to  as  great  a  tem- 
perature as  possible,  both  before  and  during  the  expansion  of 
the  air  in  the  cylinders  or  upon  the  motor  wheel. 


TABLES  FOR  THE    LOSS   OF  PRESSURE  OF 
AIR  IN   PIPES. 

In  calculating  tables  for  the  loss  of  pressure  in  pipes,  it  has 
been  found  necessary  to  take  a  wide  departure  from  the  form 
of  the  tables  usually  given  in  catalogues  on  Compressed  Air, 
and  whose  simplicity  unfortunately  does  not  agree  with  more 
recent  experimental  results  touching  upon  the  subject. 

The  formulae  from  which  such  tables  are  generally  estab- 
lished are  the  outcome  of  experiments  made  at  the  Mount 
Cenis  Tunnel,  and  of  Stockalper's  more  recent  investigations 
at  the  St.  Gothard  Tunnel. 


22  COMPRESSED   AIR. 

Similar  formulae  have  been  used,  with  some  modifications 
of  detail,  by  Professor  Riedler,  who  conducted  extensive  tests 
upon  the  compressed  air  system  in  Paris,  and  they  are  based 
on  the  assumption  that  the  loss  of  pressure  varies  directly  as  the 
length  of  the  pipe,  and  inversely  as  its  diameter. 

Professor  Unwin  took  up  the  subject,  availing  himself  of 
the  results  formerly  obtained,  and  his  investigation  of  the  laws 
governing  the  motion  of  air  in  long  pipes  does  not  support  the 
above-quoted  conclusions. 

Taking,  for  instance,  three  pipes,  each  5  inches  in  diameter, 
wherein  air  enters  at  a  pressure  of  70  Ibs.  gauge,  and  at  a 
velocity  of  20  feet  per  second,  if  one  of  these  pipes  be  one  mile 
long,  the  second  2  miles,  and  the  third  5  miles  long,  the  loss 
of  pressure  according  to  Un win's  formula  is: 

4.6  Ibs.  for  the  i-mile  pipe, 

9.4  Ibs.  for  the  2-inile  pipe, 

26.3  Ibs.  for  the  5-mile  pipe. 

In  other  words,  the  lengths  being  as:  i  -      2  5, 

the  drop  of  pressure  varies  as:  i  -  2.043  ~  5-725 

and  while  the  discrepancy  is  unimportant  for  short  lengths,  it 

becomes  14.4  per  cent  at  5  miles,  and  would  be  still  greater  for 

longer  pipes. 

As  the  logical  tendency  is  toward  increasing  the  practical 
length  of  power  transmissions,  a  saving  of  a  few  pounds  of 
loss  is  important;  consequently,  in  working  out  a  compressed 
air  transmission,  more  precise  data  are  needed.  To  meet  this  re- 
quirement, the  following  tables  were  calculated  from  Un  win's 
formula. 

From  the  preceding  example  we  notice  that  the  loss  of 
pressure  increases  more  rapidly  than  the  ratio  of  the  lengths; 
besides,  this  loss  does  not  vary  inversely  as  the  diameter  of  the 
pipe. 

Taking  a  4-inch  pipe,  2000  feet  long,  into  which  air  at  60 
Ibs.  gauge  enters  with  a  velocity  of  15  feet  per  second,  the  loss 
at  the  lower  end  will  be  7.795  Ibs.;  according  to  the  old  rule, 
the  loss  in  an  8-inch  pipe  of  same  length,  and  at  the  same 
pressure  and  velocity  of  air,  would  be  one-half  this  amount,  or 
°'S97S  Ibs.;  yet  Unwin's  rule  makes  it  0.52  Ibs. 

In  the  same  way  the  loss  in  a  1 2-inch  pipe  should  be  0.398 
Ibs.,  while  its  actual  value  is  o.j  Ibs.  Here  the  loss  of  pres- 
sure decreases  more  rapidly  than  the  diameter  increases. 

And  if  we  accept  the  theory  that  recent  rules,  when  ema- 
nating from  a  reliable  source,  are  the  best,  we  must  conclude 
that  no  satisfactory  approximation  to  exact  results  can  be  ob- 
tained with  the  proportional  formulae. 

In  the  annexed  tables,  the  air  pressure  at  the  entrance  to 
the  main  has  been  assumed  to  be  70,  80, 90,  and  100  Ibs.  gauge, 
which  figures  cover  the  working  pressures  at  which  air  will 
generally  be  admitted  to  the  motors. 

The  use  of  the  tables  involves  a  few  elementary  operations, 
which  we  have  clearly  defined  in  several  numerical  examples, 


COMPRESSED   AIR.  23 

selected  to  suggest  a  ready  method  of  solving  any  ordinary 
problems. 

Some  little  calculation  must  of  necessity  be  done,  inasmuch 
as  to  construct  a  series  of  tables,  which  would  take  into  consid- 
eration every  element  which  influences  all  cases  of  transmission, 
would  necessitate  too  much  elaboration,  and  would  not  be  de- 
sirable in  a  treatise  of  this  character. 


EXAMPLE    i. 

500  cubic  feet  of  free  air  is  compressed  per  minute  to  80  Ibs.  gauge, 
and  conveyed  through  a  6%-inc/i  pipe,  2  miles  long.  What  will  be  the 
air  pressure  at  the  lower  end  of  the  pipel 

Referring  to  Table  Fig.  5,  which  deals  with  air  compressed 
to  So  Ibs.  gauge,  and  starting  down  column  3  (size  of  pipe  in 
inches)  we  stop  at  6-%  ins.  On  the  left  side  (Col.  I)  we  find 
for  the  ratio  of  absolute  air  pressures  at  lower  and  upper  ends  of 


I — 0.00000003709  z>,    / 

(z>,  is  the  velocity  of  air  at  entrance  to  main,  in  feet  per  second, 
and  /  is  the  length  of  pipe  in  feet.) 

Following  now  the  horizontal  line  to  the  right  until  it 
meets  the  vertical  column  headed  500,  we  find  36.5  which  is  the 
value  of  vt  2. 

So  v,2  1=36.5x5280x2=385,440 
and  the  ratio  of  air  pressures  (Col.  I)  becomes: 


V 


i — 0.00000003709  X  385 , 440=0. 992 


The  pressure  at  entrance  to  main  is  80  Ibs.  gauge  or  94.7 
Ibs.  absolute;  the  pressure  at  the  lower  end  will  be: 
94. 7X0. 992  =93 .9  Ibs.  absolute 
14.7 

Or     79.2  Ibs.  gauge, 
The  loss  is:     80 — 79.2=0.8  Ibs. 


EXAMPLE   2. 

How  many  cubic  feet  of  free  air  per  minute,  compressed  to  90  Ibs. 
gauge,  can  be  conveyed  in  a  9-^  inch  pipe,  5  miles  long,  the  loss  of 
pressure  to  be  3  Ibs.? 

The  absolute  pressure  at  entrance  to  main  is:  104.7  Ibs. 
The  absolute  pressure  at  lower  end  is:  101.7    " 

Their  ratio  is:  -  °-^  =0.971 
104.7 

Referring  to  Table  Fig.  6  (90  Ibs.  gauge)  and  following  Col. 
3  down  to  9-^  inch,  we  find  on  the  left  of  this  figure  (Col.  i) 


COMPRESSED   AIR. 


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COMPRESSED   AIR. 


26 


COMPRESSED   AIR. 


COMPRESSED  AIR. 


28  COMPRP4SSKD   AIR. 

that  the  ratio  of  absolute  pressures  at  lower  and  upper  end  of 
main  is: 

-./I — 0.00000002075  z1, 2  / 

and  as  we  know  that  this  ratio  is  equal  to  0.971,  we  niay  write: 
0.971=1  A— O.COOC0002C  75  v^  *  I 

Or,  squaring  both  members  of  this  equation: 

0.9428=1 — o.  00000002075  ~z',2X  5280X5 
Or:          0.0005478  7Jk  *=i — 0.9428 

hence:     v{  '=104.4 

which  we  must  find  in  the  horizontal  column  starting  from 
9-^/x;  we  see  that  this  number  is  comprised  between  84  (2000 
cu.  ft.)  and  131.3  (2500  cu.  ft.). 

The  required  number  is  intermediate  between  2000  and  2500 
cu.  ft.;  it  can,  with  sufficient  accuracy,  be  obtained  by  interpo- 
lation: 

131.3 — 84=47.3.  Corresponding  to  a  difference  of  500  cu.  ft. 
of  free  air  (from  2500  to  2000). 

104.4 — 84=20.4,  which,  by  a  simple  rule  of  three,  corresponds 
to:  500x^3—215,  and  the  required  number  of  cubic  feet  of  free 
air  per  minute  is: 

2215. 


EXAMPLE   3. 

We  desire  to  convey  1000  cu.  ft.  of  free  air  per  minute^  com- 
pressed to  jo  Ibs.  gauge,  through  a  pipe  3  miles  long^  the  loss  in 
pressure  not  to  exceed  5  Ibs.  What  must  be  the  diameter  of  the  pipe  ? 

This  diameter  could  be  determined  directly,  but  through 
calculations  more  intricate  than  by  the  tables,  which  can  be 
used  in  the  following  manner: 

The  pressure  at  entrance  to  main  is  8.4.7  ^s-  absolute. 

The  permissible  loss  is  5. 

The  pressure  at  the  lower  end  of  main  is: 

79.7  Ibs.   absolute, 
and  the  percentage  of  loss  is: 


Referring  to  Table  Fig.  4  (70  Ibs.  gauge)  the  right  value  of 
v{  2  is  somewhere  in  the  vertical  column  headed  1000. 

The  length  is  15840  feet=/. 

We  will  try  some  values  of  z>,  3  and  apply  them  to  the  cor- 
responding ratio  of  terminal  pressures,  until  the  result  is 
exactly  or  approximately  0.94. 

If  the  result  is  not  exactly  0.94  we  will  then  take  the 
nearest  larger  commercial  size  of  pipe,  thus  giving  less  than 
5  Ibs.  loss  through  the  main. 

To   facilitate  these   approximations  we  may  remark  that, 


COMPRESSED   AIR.  29 

vising   the   formula   of  Col.   I,  we  will  have  an  expression  of 
this  form: 

0  .94—1  /i  —  o.ooooooo  *  •       *  z,-,  3  / 

in  which  the  stars  represent  some  numerical  value  to  be  dis- 
covered; or,  squaring  both  members  of  this  equation: 
o.ooooooo  *  *  *  *   z/,2  /—i  —        O-942 

=0.1164 
Let  us  try  s>,2=449,  corresponding  to  a  5-in.  pipe,  we  have 

o.  00000004972  X449  X  1  5840=0.3536 
which  result  is  much  too  large. 

We  see  that  we  have  evidently  to  take  a  smaller  value  of 
?',  3  since  /  remains  constant,  while  the  factor  corresponding  to 
4972  diminishes  with  z>,  2. 

Trying  v{  2=roo,  which  corresponds  to  a  y^-inch  pipe,  we 

0.0000000299  X  TOO  X  1  5840=0.  0474 
which  is  below  the  value  o.  1164  which  we  desire. 

Taking  i'l*==iS3,  which  corresponds  to  a  6,^-iuch  pipe,  we 
0.00000003709  X  183  XI584C—  o-i 


This  is  the  nearest  value  smaller  than  0.1164  and  will  give 
less  than  5  Ibs.  less;  and  thus  we  conclude  that  the  required 
diameter  of  pipe  is  6%  ins. 

A  short  use  of  the  tables  will  render  them  quite  convenient 
to  use: 

The  above"  three  examples  cover  the  principal  question 
liable  to  arise  in  ordinary  practise,  and  the  few  calculations 
involved  are  more  than  balanced  by  the  greater  correctness  of 
the  results  derived  from  Unwin's  formulae. 

We  can  use  the  tables  to  find  the  loss  of  pressure  incurred 
in  the  passage  of  air  through  a  pipe  of  a  given  diameter  and 
length,  and  with  a  given  velocity  of  ingress.  But  it  is  interest- 
ing to  know  at  the  same  time  the  corresponding  loss  of  power. 

With  this  object  in  view,  a  Table  (Fig.  9)  and  curves  (Fig.  8) 
are  here  given,  showing  the  ratio  of  available  power  at  full 
expansion  and  without  reheating  at  the  lower  end  of  the  main 
to  the  available  power  at  full  expansion  and  without  reheating 
at  its  entrance. 

These  curves  show  that  the  comparative  loss  of  power  is 
always  smaller  than  the  comparative  loss  of  pressure,  and  they 
will  be  found  useful  in  estimating  the  total  loss  incurred  in  a 
given  transmission. 

Bach  curve  corresponds  to  a  certain  pressure  at  the  entrance 
to  the  main,  these  pressures  being,  as  above,  70,  80,  90,  and 
100  Ibs.  gauge. 

This  addition  to  the  study  of  the  frictional  losses  is  intended 
to  dispel  the  confusion  frequently  made  between  the  loss  of 
pressure  and  the  loss  of  power,  there  being  a  common  tendency 
to  consider  those  two  terms  as  equivalent. 


COMPRESSED   AIR. 


COMPRESSED   AIR. 


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32  COMPRESSED   ATR. 

For  instance,  if  air  enters  a  pipe  at  100  Ibs.  gauge  pressure 
=  114.7  absolute,  and  is  discharged  at  80  Ibs.  gauge,  or  94,7  Ibs. 
absolute,  thus  showing  a  reduction  of  20  per  cent  of  gauge 
pressure,  it  is  popularly  and  erroneously  estimated  that  the  air 
has  lost  20  per  cent  of  its  power.  The  ratio  between  the  abso- 
lute pressures  is  9  4>Xi  4.7=*2. 5  per  cent. 

Referring  to  the  100  Ibs.  curve,  we  note  that  the  ratio  of 
pressures  0.825  lies  midway  between  92  and  94  per  cent  ratios 
of  power;  i.  e.,  corresponds  to  93  per  cent,  showing  a  loss  of 
7  per  cent  only,  instead  of  the  so-called  loss  of  20  per  cent  of 
power. 

The  explanation  of  this  is,  that,  while  the  pressure  is 
diminished,  the  volume  is  proportionately  increased,  and  the 
real  loss  of  power  is  the  work  which  the  air  could  perform  in 
expanding  isothermally  from  the  higher  pressure  to  the  lower 
pressure,  which  work  has  been  absorbed  by  friction. 

An  inspection  of  the  curves  (Fig.  8)  will  show  that  the  actual 
pressure  at  each  point  on  the  main  becomes  a  constantly 
decreasing  fraction  of  the  initial  pressure  as  the  distance  of  this 
point  from  the  entrance  becomes  greater,  and  these  variations 
of  pressure  are  figured  by  a  line  at  45  degrees  on  the  co-ordi- 
nate axes.  For  each  absolute  pressure,  the  value  of  the  avail- 
able power  at  full  expansion,  as  compared  with  the  available 
power  at  entrance,  is  carried  on  the  corresponding  ordinate, 
and  by  joining  the  ends  of  these  ordinates,  four  curves  of 
powers  have  been  drawn,  each  one  corresponding  to  one  of  the 
above-named  initial  pressures.  Although  a  limited  range  of 
initial  pressures  has  been  considered,  the  following  general 
deductions  are  suggested  by  an  inspection  of  these  curves: 

1.  So  long  as  the  fall  of  pressure  remains  below  a  certain 
value,  which,  in  the  cases  considered,  is  about  50  per  cent,  the 
loss  of  pressure  is  more  rapid  than  the  loss  of  power,  and  the 
ratio   of  powers  is  greater  than  the   corresponding   ratio   of 
pressures. 

2.  When    the    pressure    continues    to    fall    beyond    this 
value,  the  loss  of  power  becomes  more  rapid  than  the  loss  of 
pressures,  the  ratio  of  powers  remaining,  however,  greater  than 
the  corresponding  ratio  of  pressure. 

3.  When  the  absolute  pressure  in  the  main  becomes — in 
the  cases  considered — from  1 5  to  25  per  cent  of  the  initial  absolute 
pressure,  the  ratio  of  the  powers  becomes  equal  to  the  ratio  of 
the  pressures. 

4.  The   pressure   continuing   to    fall,    the   loss    of   power 
becomes  much  more  rapid  than  the  loss  of  pressure,  until  the 
pressure  is  equal  to  the  atmosphere,  when  the  available  power 
naturally  becomes  o.  and  then  negative  (a  case  which  is  not  to 
be  considered  here),  and  the  ratio  of  powers  is  smaller  than  the 
corresponding  ratio  of  pressures. 

The  inspection  of  the  curves  also  shows  that  the  relative 
deficiency  of  the  power,  as  compared  with  the  corresponding 
pressure,  occurs  more  rapidly  with  a  low  initial  pressure  than 
with  a  higher  one,  and  incidentally  confirms  the  foregone 


COMPRESSED   AIR.  33 

statement,  that,  for  a  given  initial  pressure  and  velocity  at 
entrance,  there  is  a  limit  of  length  to  each  particular  size  of 
main,  beyond  which  neither  pressure  nor  power  would  be 
obtainable  at  its  lower  end.  the  whole  pressure  having  been 
absorbed  in  overcoming  the  friction,  and  the  air  issuing  from 
the  pipe  at  atmospheric  pressure. 

And  as,  on  the  other  hand,  the  velocity  of  the  air  varies 
inversely  with  its  pressure  at  entrance,  the  desirability  of 
high  pressure  is  apparent,  either  as  permitting  the  use  of  a 
smaller  pipe  to  convey  a  given  weight  of  air,  or  as  increasing 
the  distance  at  which  a  certain  power  can  be  obtained  with  a 
given  size  of  pipe.  This  statement  refers  to  the  conveyance 
of  the  air,  and  is,  of  course,  irrespective  of  the  convenience  of 
producing  a  high  air  pressure. 


LOSS   OF   PRESSURE   IN  THE    PASSAGE    OF 
AIR    THROUGH   BENDS. 

In  addition  to  the  frictional  loss  incurred  in  the  passage  of 
nir  through  a  straight  pipe,  under  given  conditions  of  length, 
diameter,  and  velocity,  another  cause  of  resistance  is  due  to  the 
changes  of  direction  in  the  flow  of  air. 

The  bends  in  a  pipe  line  should  be  as  few  as  possible,  but 
whenever  they  are  absolutely  necessary,  as,  for  instance,  when 
leaving  the  surface  of  the  ground  to  penetrate  in  a  vertical  or 
inclined  shaft,  abrupt  bends  should  be  avoided.  The 
branching  at  right  angles  by  means  of  a  T,  so  frequently  found 
in  small-sized  steam,  air,  or  water  pipe,  should  be  absolutely 
discarded. 

Iron  pipes  of  small  size  can  easily  be  bent  to  a  larger 
radius,  and  as  to  larger  pipes,  special  elbows  should  be  used 
instead  of  the  common  fittings,  whose  radius  is  always  small 
as  compared  with  the  diameter  of  the  pipe. 

The  annexed  table  shows  that  when  the  mean  radius  of 
curvature  is  equal  to  the  diameter  of  the  pipe,  the  loss  incurred 
in  the  air  pressure  is  nearly  four  times  as  great  as  when  the 
radius  of  curvature  is  equal  to  five  diameters,  so  that  a  pipe 
line  may  be  established  with  all  possible  care  regarding  its 
diameter  and  the  velocity  of  the  air,  consistent  with  a  small 
frictional  loss,  and  much  of  the  benefit  derived  therefrom  be 
counteracted  by  the  use  of  one  or  two  short  bends. 

With  reference  to  the  table,  it  will  be  noticed  that  it 
applies  to  bends  at  a  right  angle.  When  a  smaller  or  larger 
arc  than  90  degrees  is  used,  a  sufficient  approximation  will  be 
obtained  in  figuring  the  frictional  loss  in  proportion  to  the 
length  of  arc  of  the  bend,  as  compared  with  an  arc  of  90 
degrees,  and  of  same  radius. 

If  possible,  from  15  to  20  feet  per  second  should  be  the 
average  entrance  velocity  given  to  air  in  pipes  less  than  12 
inches  in  diameter.  Above  this  the  velocity  may  be  increased, 
but  never  to  exceed  50  feet  per  second,  for  economical  use. 


34 


COMPRESSED   AIR. 


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COMPRESSED    AIR.  35 

THE   INFLUENCE  OF  THE   DIFFERENCE  OF 
LEVEL  ON  THE  USE  OF  COMPRESSED  AIR. 

The  calculations  concerning  the  applications  of  compressed 
air  are  generally  based  upon  the  standard  values  of  the  at- 
mospheric pressure  at  the  sea  level;  viz.,  14.7  Ibs.  per  square 
inch.  The  fact  that  a  large  number  of  mines  are  located 
at  a  considerable  altitude  makes  it  necessary  to  investigate  the 
influence  of  this  condition  upon  the  use  of  compressed  air,  and 
it  will  be  shown  herein  that  the  differences  of  level  are  not 
to  be  overlooked  in  designing  a  system  for  power  transmis- 
sion. The  weight  of  one  cubic  foot  of  air,  at  the  surface  of 
the  earth,  and  at  32  degrees  Fahr.,  and  when  the  barometer 
stands  at  30  inches,  is  0.0807  IDS-  The  position  of  the  mercury 
in  a  barometer  is  due  to  the  weight  of  a  column  of  air.  whose 
height  would  be  the  thickness  of  the  atmospheric  layer  that 
surrounds  the  earth,  and  as  one  cubic  inch  of  mercury  weighs 
0.491  Ibs.,  the  weight  of  a  column  of  mercury  i  inch  square 
and  30  inches  high  is  30x0.491—14.73  Ibs.  Hence  the  con- 
clusion that  a  column  of  air  i  inch  square  and  of  the  height  of 
the  atmosphere  weighs  14.7  Ibs.,  and  will  balance  the  weight 
of  a  column  of  mercury  i  inch  square  and  30  inches  high. 

The  immediate  consequence  of  this  is  that  as  we  rise  above 
the  level  of  the  sea  at  a  given  place,  the  atmospheric  pressure 
per  square  inch  must  decrease,  since  the  height  of  the  column 
of  atmosphere  pressing  on  the  mercury  of  the  barometer 
diminishes,  and  we  can  readily  calculate  that  if  the  whole  at- 
mospheric layer  were  of  equal  density,  that  is,  if  one  cubic  foot 
of  air  had  the  same  weight  at  any  altitude,  the  thickness  of 
our  atmosphere  would  be  26,208  feet,  or  4  97  miles. 

Such,  however,  is  not  the  case.  The  weight  of  one  cubic 
foot  of  air  varies  with  its  pressure  and  with  its  temperature, 
which  both  change  with  the  altitude. 

It  is  commonly  assumed,  that  at  the  same  latitude,  the 
temperature  drops  by  i  degree  Fahr.  for  every  340  feet  of 
height  above  the  sea  level;  but  this  could  not  be  taken  as  any- 
thing like  a  general  rule,  since  the  temperature  is  affected  by 
many  local  and  variable  conditions.  It  suffices,  however,  to 
show  that  the  density  of  air  changes  with  the  altitude,  but  as 
the  laws  of  this  variation  are  imperfectly  known,  and  only  for 
moderate  altitudes,  the  exact  thickness  of  the*atmospheric 
layer  that  surrounds  our  planet  is  a  matter  of  speculation.  It 
is  generally  conceded,  however,  to  be  about  45  miles. 

The  variations  of  atmospheric  pressure  with  the  altitude 
have  been,  in  the  annexed  table,  calculated  from  the  sea  level 
to  10,000  feet  above  it,  and  for  equal  steps  of  500  feet,  on  the 
assumption  of  a  constant  temperature  of  60  degrees  Fahr.  pre- 
vailing throughout  the  change  of  altitude.  This  supposition, 
however,  as  we  have  mentioned  before,  is  not  correct,  but  the 
exact  influence  of  the  temperature  can  easily  be  computed  for 
any  particular  instance. 


36  COMPRESSED   AIR. 

An  inspection  of  the  table  of  atmospheric  pressures  leads  to 
an  immediate  practical  conclusion.  L,et  us  take,  for  instance, 
a  machine  designed  to  compress  at  the  sea  level  500  cubic  feet  of 
free  air  per  minute  to  80  Ibs.  gauge,  that  is,  80  Ibs.  above  the 
atmospheric  pressure.  The  volume  of  cold  compressed  air  de- 
livered per  minute  is 

500x^=77.6  cu.  ft. 

Suppose  now  that  the  same  compressor  be  used  at  5000  feet 
altitude  and  run  at  the  same  number  of  revolutions;  the  piston 
will  sweep  through  500  cubic  feet  as  before,  but  the  atmos- 
pheric pressure  being  only  12.14  Ibs.  per  square  inch,  the 
volume  of  cold  air  at  80  Ibs.  gauge  delivered  per  minute  will  be 

500x^=65.85  cu.  ft. 

That  is  to  say,  the  delivery  of  air  at  80  Ibs,  gauge  and  at  5000 
feet  altitude  will  be  85  per  cent  of  the  delivery  at  80  Ibs.  gauge 
and  at  the  sea  level,  from  the  same  sized  compressor  running 
at  the  same  number  of  revolutions. 

These  volumetric  variations,  reckoned  upon  the  volume  at 
the  sea  level  taken  as  a  unit,  will  be  found  recorded  in  four 
columns  corresponding  respectively  to  70,  80,  90,  and  100  Ibs. 
gauge  and  annexed  to  the  pressure  column.  It  will  be  noticed 
that  the  volumetric  efficiency,  that  is  the  ratio  of  the  delivery 
at  any  given  altitude  to  the  delivery  at  the  same  pressure  and 
at  the  sea  level,  decreases  as  the  receiver  pressure  increases. 

We  know  that  in  adiabatic  compression  (which  we  may 
take  as  a  standard  of  comparison)  the  compression  to  80  Ibs. 
gauge  and  delivery  of  500  cu.  ft.  of  free  air  per  minute  absorbs 
79.4  I.  H.  P.  It  may  easily  be  calculated  that  for  the  same 
outside  temperature  (60  degrees  Fahr.)  and  the  same  gauge 
pressure  (80  Ibs.)  the  compression  and  delivery  at  5000  feet 
altitude  of  the  same  amount  of  atmospheric  air  will  absorb 
73.7  I- H.  P. 

The  ratio  of  these  powers  is  —=.928. 

That  is  to  say,  we  lose  in  capacity  15  per  cent  and  we  gain  in 
power  7.2  per  cent,  which  amounts  to  saying  that  the  produc- 
tion at  the  same  volume  of  air  at  the  same  effective  pressure 
will  require: 

i        I.  H.  P.  at  the  sea  level, 
1.093      "         at  5000  feet, 
1.190      *'         at  10,000  feet  altitude. 

It  costs  more,  therefore,  to  obtain  the  same  useful  work  from  a 
given  compressor  at  high  altitudes  than  at  the  sea  level. 

Four  columns  of  I.  H.  P.,  referring  to  the  compression  of 
100  cubic  feet  of  free  air  per  minute  to  70,  80,  90,  and  100  Ibs. 
respectively,  are  recorded  alongside  of  the  volumetric  results. 
An  inspection  of  the  table  shows  that  if  we  compare  the  work 
absorbed  by  I  cu.  ft.  of  air  delivered  at  a  given  pressure,  at 
10,000  feet  altitude  for  instance,  and  at  the  sea  level,  the  ratio 
will  be  practically  the  same  within  the  whole  range  of  pres- 
sures considered. 


COMPRESSED   AIR. 


37 


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38  COMPRESSED   AIR. 

This  is  not  the  only  effect  of  a  difference  of  altitude  and 
a  practical  case  will  illustrate  another  side  of  the  question: 

Suppose  that  a  mining  plant  is  located  1500  feet  above  the 
Compressor  plant,  and  that  the  Compressor  plant  itself  is 
situated  at  an  altitude  of  3000  feet  above  the  sea  level,  and 
that  the  receiver  pressure  at  the  compressor  is  80  Ibs.  The 
atmospheric  pressure  at  the  elevation  of  3000  feet  in  the  Com- 
pressor room  is  13.1  Ibs.  per  square  inch.  One  cubic  foot  of 
air  at  the  sea  level,  and  at  60  degrees  Fahr.  weighs  0.0764  Ibs. 
One  cubic  foot  of  air  at  3000  feet  elevation  and  60  degrees 
Fahr.  will  weigh 

13  1 

0.0764x^=0.0681  Ibs. 

Or,  i  Ib.  of  air  will  represent  a  volume  of  14.68  cubic  feet. 
This  volume  represents  a  vertical  column  one  inch  square  and 
2113.92  feet  high  at  the  pressure  of  13.1  Ibs.  per  square  inch, 
and  at  a  pressure  of  80  Ibs.  gauge  or  93.1  Ibs.  absolute,  the 
height  of  this  column  weighing  i  Ib.,  and  i  inch  square  in 
section  is 

2113.92x^=298.06  ft. 

Consequently  a  column  of  air  at  80  Ibs.  pressure,  1500  feet 
high,  represents  a  pressure  of  5.03  Ibs.  per  square  inch. 

The  absolute  pressure  of  air,  which  at  the  lower  end  of  the 
pipe  is  93.1  Ibs.,  is  at  the  upper  end: 

93.1 — 5.03=88.07  absolute. 

and  as  the  atmospheric  pressure  at  4500  ft.  is  12.37  Ibs.  the  ef- 
fective pressure  at  the  hoisting  works  is  88.07 — 12-37  ^s-.  or 
75.7  Ibs.  So  there  is,  regardless  of  the  loss  due  to  friction  in 
this  respect,  no  loss  of  volume,  but  a  loss  of  pressure. 

A  very  similar  course  of  reasoning  would  show  that  when 
compressed  air  is  carried  down  a  shaft  the  pressure  at  the 
lower  end  is  greater  than  the  receiver  pressure,  and  this  excess 
of  pressure,  due  to  the  weight  of  this  column  of  air,  will 
generally  more  than  balance  any  friction al  losses  there  may  be 
in  the  pipes. 

It  must  be  remembered,  in  this  connection,  that  any  motors 
operated  by  this  compressed  air  will  also  have  a  larger  back 
pressure  to  encounter  in  the  exhaust  than  they  would  at  the 
mouth  of  the  shaft,  but  still  the  loss  due  to  this  back  pressure 
is  only  a  small  portion  of  the  gain  by  the  difference  of  level. 

In  both  of  these  examples  an  exact  computation  would  re- 
quire a  consideration  of  the  temperature,  but  which  may  be 
neglected  in  all  ordinary  propositions. 


AIR   ENGINES. 

Compressed  Air,  like  all  elastic  gases,  can  be  made  to  oper- 
ate a  piston  by  its  expansive  force,  exactly  as  does  steam,  and 
it  may  be  stated  in  a  general  way,  that  any  steam  engine  can 
be  actuated  by  air  without  altering  its  arrangement.  It  is, 


COM  PRESSED   AIR.  39 

moreover,  hardly  necessary  to  add  that  this  statement  applies 
to  the  non-condensing  steam  engines  only. 

Tables  are  herewith  given  of  the  consumption  of  air  per 
minute,  reduced  to  atmospheric  pressure,  in  three  classes  of 
engines  more  commonly  used;  viz: 
The  Slide  Valve  Engine, 

The  Automatic  Cut-off  Engine,  Single  and  Compound, 
The  Corliss  Engine,  Single  and  Compound. 

Air  and  Steam,  however,  while  partaking  of  the  same  gen- 
eral active  property,  differ  widely  in  several  respects,  and  a  few 
explanatory  remarks  are  here  necessary. 

In  the  first  place,  the  pressure  of  air  may  be  independent  of 
its  temperature.  This  valuable  feature,  which  makes  other- 
wise the  use  of  compressed  air  so  convenient,  is  fraught,  how- 
ever, with  practical  consequences  which  in  many  cases,  and 
unless  provided  for,  would  render  it  impossible. 

Air,  in  most  cases,  expands  in  a  motor  adiabatically;  i.  e.,  its 
expansion  is  accompanied  by  a  considerable  fall  of  tempera- 
ture. An  additional  table  is  here  presented  (Fig.  19),  giving 
the  temperature  of  exhaust  of  air,  after  working  expansively  in 
the  various  types  of  engines  considered.  This  temperature  is 
found  to  range"  from  +7.5  in  the  slide  valve  engine  to  — 143  in 
the  Compound  Corliss,  cutting  off  at  l/z  of  stroke,  the  air  being 
admitted  to  the  engine  at  60  degrees  Fahr.,  and  while  the  for- 
mer temperature  might  not  prove  troublesome  with  dry  air,  on 
account  of  the  strong  exhaust  blast  of  an  engine  with  a  late 
cut-off,  the  latter  is  decidedly  unacceptable,  as  any  lubricant 
introduced  in  the  cylinder  would  freeze  instantly,  and  the 
exhaust  ports  be  promptly  clogged  with  ice,  especially  in  the 
interior  of  a  mine  where  the  moisture  of  air  is  more  marked 
than  outside. 

It  will  therefore  be  necessary  for  the  economical  use  of  air 
to  heat  it  to  a  certain  extent,  either  before  it  enters  the  motor, 
or  during  the  process  of  its  expansion  within  the  cylinder. 
We  know  already  that  this  operation  has  also  the  effect  of  in- 
creasing the  volume  of  the  air  at  constant  pressure.  *Two 
curves  are  here  presented  showing  the  increase  of  volume  of  I 
cubic  foot  of  air,  at  32  degrees  Fahr.  and  at  60  degrees  Fahr., 
when  heated  to  various  temperatures  up  to  500  degrees  Fahr. 

In  connection  with  this  subject  of  re-heating,  another  dis- 
tinctive feature  of  air  as  compared  with  steam  must  be  pointed 
out. 

In  all  non-condensing  steam  engines,  even  with  an  early 
cut-off,  the  proportions  are  such  as  to  maintain  at  the  end  of 
the  period  of  expansion,  a  sufficient  steam  pressure  to  insure 
a  speedy  exhaust  of  the  gaseous  and  of  the  condensed  steam. 
This  pressure  must  of  course  be  greater  in  a  fast  moving  than 
in  a  slow  engine,  with  the  consequence  that  part  of  the  energy 
of  the  steam  is  thus  sacrificed,  not  uselessly,  indeed,  but  with- 
out doing  useful  work. 

But  with  air,  there  is  no  condensation  during  the  expansion, 
and  also  the  active  gas  which  operates  the  piston  being  the 


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46  COMPRESSED   AIR. 

same  as  the  medium  into  which  it  is  discharged,  the  exhaust 
pressure  may  become  a  very  insignificant  quantity. 

The  result  of  this  is  two-fold:  First,  an  air  motor,  unlike  a 
steam  engine,  can  work  practically  at  complete  expansion,  i.  e., 
the  compressed  air  can  expand  into  the  cylinder  down  to 
atmospheric  pressure;  and  second,  this  more  prolonged  ex- 
pansion will  be  accompanied  by  a  greater  fall  of  temperature. 
So  that  it  may  be  said  that  the  genuine  air  motor  is  inseparable 
from  a  system  of  reheating,  and  also  that  the  complete  ex- 
pansion of  the  air  producing  a  greater  variation  of  load  on  the 
piston,  and  of  strains  on  the  pieces,  an  air  motor  should  not 
necessarily  but  preferably  be  a  compound,  rather  than  a  single 
machine.  For  similar  reasons  it  may  rationally  be  expected 
that  turbo-motors  of  the  Parsons'  type  and  DeLaval  Rotary 
Engines  would  be  especially  well  adapted  to  show  a  high 
efficiency  as  air  motors. 

It  may  be  inferred,  that  while  an  ordinary  steam  engine  will 
perform  satisfactory  duty  if  operated  with  air,  a  less  consump- 
tion of  it  will  be  obtained  by  cutting  off  earlier  in  the  stroke 
so  as  to  work  at  complete  expansion.  This  will  diminish  the 
mean  effective  pressure  throughout  the  stroke,  and,  conse- 
quently, the  power  developed  by  the  engine,  at  the  same  time 
extending  the  range  of  variation  of  the  strains. 

Such  a  state  of  affairs  may  be  acceptable  if  the  load  on  the 
motor  is  regular,  but  if — as  will  often  be  the  case,  especially  in 
mining  machinery — the  load  constantly  varies  or  else  is  inter- 
mittent, the  air  motor  at  complete,  expansion  must  have  its 
valve  gear  so  arranged  as  to  permit  a  later  cut-off  and,  of 
course,  a  greater  or  smaller  amount  of  exhaust  pressure,  which 
amounts  to  saying  that  it  must  be  an  ordinary  steam  engine 
susceptible  of  an  earlier  cut-off  than  is  commonly  used  with 
steam. 

Reverting  now  to  the  subject  of  reheating,  several  systems 
have  been  suggested  and  used. 

If  the  only  object  was  to  preclude  the  obstruction  of  the 
exhaust  ports  by  the  formation  of  ice  due  to  the  moisture  of 
air,  it  would  be  obtained  by  the  application  to  this  portion  of 
the  engine,  of  some  source  of  heat,  such  as  a  lamp,  or  an 
injection  of  steam,  or  of  hot  water. 

This  process,  however,  hardly  deserves  more  than  a  mere 
mention,  for  if  such  a  source  of  heat  is  handy,  it  can  be  used 
to  far  better  advantage  in  heating  the  air,  either  in  the  cylinder 
or  before  entering  it. 

One  method  consists  in  injecting  into  the  cylinder  a  spray 
of  warm  water,  whose  heat  is  absorbed  by  the  air,  while  the 
water  is  cooled.  The  annexed  table  gives  the  weight  of  water 
at  75  degrees,  100  degrees,  and  150  degrees  Fahr.  to  be  supplied 
for  each  pound  of  air  expanding  to  the  atmospheric  pressure 
from  70,  80,  90,  and  100  Ibs.  gauge,  so  that  the  final  tempera- 
ture of  air  will  be  32  degrees  Fahr.,  its  initial  temperature 
being  60  degrees  Fahr. 


COMPRESSED   AIR. 


47 


Gauge 
pressure  of 
air. 

B.  T.  U. 

required    per 
Ib.  of  air. 

Pounds  of  water  per  Ib.  of  air,  the 
temperature  of  water  being 

75°  Fahr. 

100°  Fahr. 

150°  Fahr. 

Ibs. 

(A) 

Ibs. 

Ibs. 

Ibs. 

70 

59- 

1-37 

.86 

•5 

80 

62.8 

1.46 

.92 

•53 

90 

66.2 

1-54 

•97 

.56 

100 

69.2 

1.61 

1.02 

.6 

Another  and  better  method  is  to  inject  steam  instead  of 
hot  water  into  the  cylinder.  The  advantages  of  this  system 
are,  first  that  steam,  being  in  a  gaseous  state,  mixes  up  with  air 
more  readily  than  water,  even  finely  pulverized,  and  besides, 
the  condensation  of  this  steam  gives  up  its  latent  heat,  which 
increases  considerably  the  heating  of  air. 

A  comparison  of  this  process  with  the  previous  one  can 
readily  be  made.  Assuming  that  a  spray  of  water  at  212  de- 
grees Fahr.  is  injected  iuto  the  cylinder,  each  pound  of  this 
water  will  give  up  180  B.  T.  U.  before  it  is  cooled  to  32  degrees 
Fahr. 

But,  taking  steam  at  atmospheric  pressure,  i.  e.,  also  at  212 
degrees  Fahr  ,  i  Ib.  of  steam,  in  the  process  of  liquefaction, 
will  abandon  966  B.  T.  U.,  its  latent  heat  of  vaporization,  and 
besides  180  B.  T.  U.  as  above,  making  a  total  of  1146  B.  T.  U. 

The  following  table  gives  the  weight  of  steam  at  212  degrees 
Fahr.  required  for  each  pound  of  air  to  prevent  its  temperature 
from  falling  below  32  degrees  Fahr.  at  complete  expansion. 


Gauge  pressure  of  air. 


70 

80 

90 

100 


B.  T.  U.  required  for 
each  Ib.  of  air. 

59-0  

. ...  62.8  

66.2  ....... 

69.2  


ybs.  of  steam  at  212  de- 
grees per  Ib.  of  air. 

051  ....... 

055  ....... 

059  ....... 

0604  ....... 


It  is  evident  that  quite  similar  calculations  could  be  made 
to  maintain  the  exhaust  temperature  at  any  given  point.  Be- 
sides, the  use  of  steam  keeps  the  walls  of  the  cylinder  wet.  and 
while  water  alone  is  a  poor  lubricant  between  metallic  surfaces, 
it  facilitates  the  action  of  the  regular  lubricants,  and  is  also 
favorable  to  the  tightness  of  the  piston  packing. 

It  will  readily  be  seen  that  both  these  methods  completely 
preclude  the  formation  of  ice  in  the  exhaust  ports;  their  good 
effect  is  still  more  pronounced  if  the  cylinder  is  provided  with 
a  jacket,  into  which  hot  air  is  circulated. 


48 


COMPRESSED   AIR. 


COMPRESSED   AIR.  49 

Air  can  also  be  reheated  before  being  admitted  into  the 
cylinder.  Various  designs  of  heaters  are  used  for  this  purpose, 
the  air  generally  passing  through  a  system  of  pipes  heated  by 
an  interior  furnace,  a  flue  being  provided  for  the  passage  of  the 
hot  gases  on  the  outside  of  the  pipes  before  they  reach  the 
chimney.  And  as  air,  on  account  of  its  bad  conductivity,  does 
not  easily  take  up  heat  from  the  metallic  sides  of  the  pipes,  it 
is  expedient  to  inject  in  the  pipes  a  small  quantity  of  water 
which  absorbs  the  heat  more  readily  and  penetrates  with  the 
hot  air  into  the  cylinder. 

Another  method  of  heating  is  to  place  a  lamp  or  gas  jet 
within  the  air  pipe.  The  use  of  coal  or  wood  is  not  advisable 
in  this  case,  as  grit  and  cinders  would  be  carried  by  the  current 
of  air  into  the  motor. 

Reheating  by  the  electric  current  is  still  in  the  experimental 
state. 

When  the  motor  is  a  compound  machine,  the  air  should  be 
again  reheated  after  it  has  done  work  in  the  H.  P.  cylinder, 
and  before  it  is  admitted  to  the  L.  P.  cylinder. 

The  table  giving  the  temperatures  of  exhaust  in  cold  air 
work,  also  gives  the  temperatures  at  which  air  should  be 
reheated  prior  to  its  admission  to  the  single  engines,  or  to  each 
cylinder  of  the  compound  engines,  in  order  to  exhaust  at  32 
degrees  Fahr. 

These  temperatures  are  moderate,  and  can  be  obtained  with 
hot  water,  or  low  pressure  steam.  If  the  heating  is  done  by 
passing  the  air  through  heated  pipes,  the  fuel  consumption 
will  be  very  small,  as  practise  shows  that  i  Ib.  of  coal  gives  the 
air  from  8,000  to  10,000  B.  T.  U.  in  a  properly  designed 
beater. 

To  utilize  the  full  benefit  of  reheating,  and  of  air  expansion  in 
compound  engines,  an  early  cut- off  is  very  desirable.  This 
can  be  accomplished  by  reheating  to  350  degrees  before  the  air 
enters  each  cylinder,  and  Table  Fig.  20  shows  the  amount 
of  free  air  required  for  various  horse  powers  under  this  condi- 
tion. A  comparision  with  Table  Fig.  16  will  show  the 
marked  advantage  of  this  arrangement. 

Fig.  20^  shows  a  compound  direct  connected  Corliss 
Hoisting  Engine,  built  by  the  Fulton  Engineering  and  Ship- 
building Company,  in  conformity  with  the  data  in  Fig.  20. 
The  air  is  twice  reheated;  that  is  to  say  before  entering  the 
high  pressure  cylinder,  and  also  before  entering  the  low  pres- 
sure cylinder. 

For  convenience  in  estimating  the  power  required  to  com- 
press air  and  the  amount  of  air  which  will  be  furnished  by 
given  powers,  the  following  tables  have  been  constructed: 

The  table  in  Fig,  21  shows  the  amount  of  cubic  feet  of  free 
air  at  60  degrees  Fahr.  and  14.7  Ibs.  absolute  pressure  per 
square  inch,  that  can  be  compressed  and  delivered  per  minute 
per  I.  H.  P.,  adiabatically,  in  a  single  stage  jacketted  cylinder 
compressor,  in  a  two-stage  compound  jacketted  compression 
and  in  isothermal  compression. 


COMPRESSED  AIR. 


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COMPRESSED   AIR. 


COMPRESSED   AIR.  55 

This  table  is  constructed  from  the  curve  represented  in 
Fig.  22. 

In  the  table  the  amount  of  air  is  given  for  each  indicated 
horse  power  in  the  air  cylinder  and  also  for  each  I.  H.  P.  in 
the  direct-acting  steam  cylinder  which  drives  the  compressor. 

The  table  in  Fig.  23  is  practically  the  reverse  of  the  pre- 
ceding curve  and  the  table  gives  the  I.  H.  P.  to  compress  and 
deliver  100  cubic  feet  per  minute  of  air,  at  60  degrees  Fahr.  and 
14.7  Ibs.  per  square  inch  absolute  pressure.  This  table  is  con- 
structed from  the  curve  (Fig.  24)  and  gives  the  I.  H.  P.  in  the 
adiabatic  compression,  in  single  stage  jacketed  cylinder  com- 
pression, in  two-stage  compound  jacketed  compression  and 
also  isothermal  compression,  and  the  horse  powers  under  each 
of  the  different  gauge  pressures  read  both  for  the  I.  H.  P.  in 
the  air  cylinder  and  the  I.  H.  P.  in  the  direct-acting  cylinder. 

Fig.  25  is  the  curve  of  mean  effective  pressures  per  square 
inch  in  adiabatic  compression,  for  the  various  receiver  pres- 
sures enumerated.  This  will  be  found  useful  in  computing 
piston  loads. 

Fig.  26  is  a  table  of  pressures  per  square  inch,  due  to  the 
weight  of  air  at  60  degrees  Fahr.  in  vertical  pipes,  and  also  the 
weight  of  one  cubic  foot  of  air  in  pounds  avoirdupois.  For 
example,  if  the  gauge  pressure  at  the  surface  of  a  mine  is  70 
Ibs.  per  square  inch,  at  the  depth  of  one  thousand  feet  the 
pressure  will  be  73  Ibs.  to  the  square  inch.  Where  there  are 
extreme  variations  in  altitude  in  a  transmission  plant  this 
weight  of  air  has  to  be  taken  into  consideration. 


COMPRESSED   AIR. 


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COMPRESSED   AIR. 


AMOUNT  OF  FREE  AIR  REQUIRED  TO  RUN 
DIRECT-ACTING  STEAM   PUMPS. 

In  preparing  these  tables  the  object  has  been  to  furnish 
information  to  the  oft-repeated  query,  "How  many  cubic  feet 
of  free  air,  compressed  to,  say  60  Ibs.,  is  required  to  run  a 
direct-acting  pump  that  will  raise  50  gals,  per  minute  200  feet 
high,  or  say  8  miners'  inches  150  feet  nigh,  or  at  any  other 
pressure  of  air  ?"  We  have  made  three  assumptions  in  these 
calculations,  which  are  likely  to  cover  all  possible  losses  of 
efficiency  in  ordinary  work. 

First — The  work  absorbed  by  the  pump  has  been  estimated 
by  adding  20  per  cent  to  the  actual  work  in  water  raised,  to 
make  up  for  frictional  and  other  resistances. 

Second — The  actual  capacity  of  the  air  cylinder,  that  is,  the 
volume  swept  by  the  piston,  has  been  increased  by  15  per  cent 
to  take  into  account  the  clearance,  leakage,  etc. 

Third — The  working  pressure  of  air,  when  entering  the  air 
cylinder,  has  been  taken  at  10  Ibs.  per  square  inch  lower  than 
the  receiver  pressure,  to  compensate  for  frictional  and  other 
resistances. 

We  have  not  assumed  that  the  air  was  reheated  before 
entering  the  cylinder,  nor  was  any  account  taken  of  the  differ- 
ence of  level  between  the  receiver  and  the  pump,  which  in 
many  cases  would  add  several  pounds  per  square  inch  to  the 
working  pressure,  as  noted  in  the  Table  (Fig.  26).  The 
results  given  in  these  tables  may  therefore  be  referred  direct  to 
the  intake  capacity  of  the  compressor  and  the  estimate  of  the 
air  consumption  required  is  therefore  very  much  simplified. 

If  the  necessary  power  to  produce  the  quantities*  of  com- 
pressed air  indicated  in  these  tables  be  compared  to  the  cor- 
responding work  in  water  raised,  the  efficiency,  which  is 
measured  by  the  ratio  of  the  latter  to  the  former,  will  be  as 
low  as  25  per  cent.  A  direct-acting  pump  does  not  use  air 
expansively,  and  this  is  well  known  to  be  a  simple  but  a  waste- 
ful manner  of  transmitting  power. 

Assuming  the  values  in  these  tables  to  be  one,  the  follow- 
ing table  will  show  the  percentages  required  for  the  different 
kinds  of  power-actuated  pumps,  both  for  cold  air  and  air 
delivered  at  300  degrees  Fahr.  at  the  pump  motor. 


Kind,  of"  Motor 

AI 

R. 

Cold.   (60°  F.) 

Reheated  to 
300°  F. 

Direct  Acting  Single.          .    .,    .    ... 

j 

6Q 

Direct  Acting  Compound  

70  to   60 

•  y 

48  to   41 

(  Slide  Valve  Single  
FlyWheel  -(Slide  Valve  Compound 
f  Corliss  Compound   

.60 
.50 

•33 

.41 

.329 
.226 

COMPRESSED   AIR. 


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IB  COMPRESSED   AIR.  63 

REFRIGERATION    BY   COMPRESSED    AIR. 

This  Treatise  would  soon  grow  beyond  reasonable  limits  if 
it  had  to  enumerate  all  the  applications  of  compressed  air  in 
modern  industry;  in  fact,  a  publication  claiming  to  give  an 
exact  "  up  to  date"  account  of  these  applications  would  never 
come  to  an  end,  as  some  new  and  unexpected  uses  are  con- 
stantly arising. 

But  a  review,  however  cursor}-,  of  the  properties  of  com- 
pressed air  considered  as  motive  power,  must  of  necessity 
touch  upon  one  of  its  most  interesting  uses;  viz.,  the  produc- 
tion of  cold.  A  rapid  treatment  of  this  question  is  here  the 
more  justified  as  it  does  not  correspond  to  a  class  of  apparatus 
intended  solely  for  refrigerating  purposes. 

Every  air  motor  is  in  itself,  and  at  no  additional  cost,  a 
cold-producing  machine,  and  this  property,  which  belongs 
exclusively  to  compressed  air,  will  often  be  found  a  valuable 
addition  to  its  other  merits,  especially  by  the  underground 
worker. 

A  quotation  from  Prof.  A.  B.  W.  Kennedy  on  the  Paris  air 
installations  may  fitly  be  reproduced  here: 

"By  using  air  direct  from  the  main  in  the  motor,  or  by 
heating  it  only  very  slightly,  the  exhaust  air  can  be,  of  course, 
so  greatly  reduced  in  temperature  as  to  be  available  for  freez- 
ing purposes. 

"In  one  Paris  restaurant,  for  instance,  which  I  visited,  I 
found  that  the  exhaust  was  carried  through  a  brick  flue  into 
the  beer  cellar.  In  this  flue  the  carafes  were  set  to  freeze, 
large  molds  of  block  ice  were  also  being  made  for  table  use, 
while  the  air  was  still  cold  enough  in  passing  away  through 
the  beer  cellar  to  render  the  use  of  ice  for  cooling  quite  un- 
necessary even  in  the  hottest  weather. 

' '  The  nominal  function  of  the  engine  in  this  case  was  the 
charging  of  batteries  used  in  the  electric  lighting  of  the 
restaurant. 

"  The  conjoint  use  of  power  and  cold  is  common  in  Paris, 
the  power  being  in  this  case  generally  applied  to  electric 
lighting.  While  in  any  large  city,  such  as  Paris,  it  is  no  doubt 
a  great  point  that  by  a  compressed  air  system  the  handiest 
possible  cooling  appliances  can  be  brought  everywhere  within 
reach,  in  tropical  climates  this  is  something  rather  of  necessity 
than  of  luxury.  In  such  cases  we  might  have  the  apparent 
paradox  of  a  motor  worked  essentially  for  its  exhaust;  the 
work  done  would  be  a  bye-product,  the  cold  air  would  be  the 
principal  thing. 

"  In  such  a  case,  if  there  were  no  useful  work  to  be  done,  the 
motor  could  even  be  made  (as  has  been  suggested  to  me)  to 
pump  air  back  into  the  main,  and  thus  to  virtually  halve  its 
air  consumption." 

From  these  remarks  the  conclusion  is  obvious  that  ice- 
making,  water-cooling,  and  cold-storage  contrivances  are  of 
easy  application  whenever  air  motors  are  used;  and  it  will  be 


64  COMPRESSED   AIR. 

readily  understood  that  the  exhaust  temperature  of  air  may  be 
regulated  by  a  variation  in  the  degree  of  heating. 

An  inexpensive  and  tolerably  efficient  arrangement  consists 
of  exhausting  the  air  from  the  motor  at  one  end  of  a  duct 
made  of  insulating  material,  such  as  two  or  more  parallel 
courses  of  one-inch  boards,  paper-coated  on  the  outside,  and 
secured  one  or  two  inches  apart  by  wooden  strips;  or,  else,  in  a 
more  permanent  installation  the  duct  may  be  a  brick  flue, 
such  as  described  in  the  above  report. 

In  both  cases  its  upper  portion  can  be  laid  open,  and 
arrangements  are  made  at  the  interior  of  it  for  suspending  ice 
molds,  water  pails,  etc.,  which  are  removed  at  intervals 
depending  upon  the  exhaust  temperature  of  the  motor  and  its 
activity. 

Provision  should  be  made  to  rid  the  exhaust  air  from  all  the 
grease  or  oil  which  it  might  carry  out  of  the  motor  before  it  is 
admitted  into  the  duct. 

One  noteworthy  feature  about  air  thus  used  for  cooling 
purposes  is  its  wholesome  nature;  with  its  defects,  adiabatic 
compression  is  endowed  with  this  beneficial  property  that  the 
combined  heat  and  pressure  thus  generated  prove  too  much 
for  the  endurance  of  microbes;  air  thus  treated  becomes  thor- 
oughly sterilized,  and  can  be  safely  put  in  contact  with 
alimentary  substances  at  no  risk  of  contamination.  In  fact, 
fruits  are  wonderfully  preserved  during  transportation  by  a 
new  system  wherein  the  exhaust  from  the  air  brake  cylinders 
is  the  vital  principle. 

More  elaborate  ice-making  or  cold-storage  appliances  might, 
of  course,  be  devised,  and  special  machinery  has  been  con- 
structed to  that  effect. 

It  is  not  here  intended  to  treat  upon  the  general  subject  of 
ice-making  machines.  This  cannot  be  done  in  an  elementary 
way  with  any  degree  of  completeness.  Referring  solely  to  the 
air  machine,  it  may  be  stated  that  it  is  not  the  most  economical 
for  cold  production,  but  in  many  instances  it  remains  in  use 
because  of  its  convenience  and  safety. 

Air  is  found  everywhere,  and  in  case  of  leakage  is  not  apt, 
like  ammonia  or  sulphur  dioxide,  to  spoil  the  provisions  sub- 
jected to  cooling. 

The  developments  previously  expounded  in  this  treatise 
will  facilitate  the  comprehension  of  the  cold  air  machine, 
which  is  principally  used  on  shipboard,  for  the  preservation  of 
provisions,  and  for  ice-making. 

Two  principal  types  of  machines  are  commonly  used. 

THE  BEU/-COLEMAN  MACHINE. 

A  revolving  shaft  d,  is  operated  either  by  a  steam  engine  S, 
and  a  crank  <:,  as  shown  on  the  line  drawing,  or  by  a  belt 
transmission. 

This  shaft  carries  two  flywheels  Wy  W,  and  two  opposite 
cranks  e,  /,  actuating  by  connecting  rods  and  crossheads  two 
pistons  v,  h. 


COMPRESSED  AIR. 


66  COMPRESSED  AIR. 

The  piston  h  travels  in  a  cylinder  g,  which,  for  the  sake  of 
simplicity,  has  been  shown  single-acting.  The  piston  h  is 
solid,  and  the  back  head  of  the  cylinder  carries  two  automatic 
valves  t,  K.  The  valve  z,  opening  inward,  is  an  inlet  valve 
admitting  the  free  air  into  the  cylinder,  during  one  stroke  of 
the  piston  h;  during  the  reverse  stroke  the  valve  i  is  closed, 
the  air  confined  in  the  cylinder  is  compressed,  and  escapes 
through  the  outlet  valve  K^  and  the  pipe  /,  into  a  tubular 
cooler,  through  which  a  series  of  tubes  /,  establishes  a  contin- 
uous circulation  of  cold  water.  This  water  enters  the  cooler 
through  the  cover  ;«,  and  is  discharged  through  the  opposite 
end  n. 

The  air  delivered  by  the  compressing  cylinder  g,  passes 
around  the  tubes  /,  is  cooled  to,  or  nearly  to,  the  outside  tem- 
perature, and  passes  through  the  pipe  0,  connected  to  the 
backhead  of  another  cylinder  «. 

This  cylinder,  which  is  also  shown  single-acting,  has  a 
solid  piston  vt  operated  by  the  crank  e;  the  backhead  carries 
two  separate  and  closed  chambers,  containing  one  an  inlet 
valve  p,  and  the  other  a  discharge  valve  q;  but  instead  of 
acting  automatically,  these  valves  have  their  motion  controlled 
by  two  adjustable  cams  revolving  within  the  shaft  d,  as  shown 
on  the  cut. 

While  the  compression  cylinder  g  delivers  at  each  stroke 
some  compressed  air  into  the  cooler,  the  inlet  valve  p  admits 
into  the  cylinder  q  a  certain  volume  of  this  air,  which,  as  said 
before,  has  been  cooled  on  its  passage  around  the  tubes,  but 
the  setting  of  the  cam  operating  the  valve  /  on  the  shaft  is  so 
arranged  as  to  close  this  valve  long  before  the  piston  v  is  at 
the  outer  end  of  its  stroke;  the  volume  of  air  introduced  into 
the  cylinder  u  is  then  left  to  expand  adiabatically,  and  its 
temperature  falls  to  a  point  which  depends  upon  the  amount  of 
expansion,  i.  e.  upon  the  quantity  of  air  admitted  by  the 
valve/;  besides,  this  work  of  expansion  helps  the  motion  of 
the  machine  to  some  extent.  For  this  reason,  the  cylinder  u  is 
called  the  expansion  cylinder. 

When  the  piston  v  has  reached  the  end  of  its  stroke,  the 
discharge  valve  q  is  opened  by  its  cam,  and  so  remains  during 
the  whole  reverse  stroke,  the  piston  v  driving  the  cold  air 
through  the  pipe  r,  to  the  cold  storage  rooms. 

It  will  be  readily  understood  that  when  the  valve  /  closes 
early  on  the  stroke  of  the  expansion  piston  v,  the  pressure  in 
the  cooler  increases,  and  the  exhaust  temperature  in  the  cylin- 
der u  decreases;  when,  on  the  contrary,  the  closing  of  the 
valve  p  is  retarded,  the  pressure  in  the  cooler  drops,  and  the 
exhaust  temperature  rises.  So  that,  by  a  proper  adjustment  of 
the  cams,  the  degree  of  cooling  air  can  be  varied  within  a  large 
range. 

This  machine  is  comparatively  cumbersome,  if  the  amount  of 
cooling  is  important. 


COMPRESSED   AIR.  67 

THE  ALLEN  DENSE-AIR  MACHINE. 

To  obviate  this  defect,  another  class  of  machines  has  been 
devised,  known  as  the  AI<I<EN  DENSE-AIR  MACHINE.  Its  gen- 
eral arrangement  being  practically  the  same,  no  special  draw- 
ing of  it  is  given. 

The  air  penetrating  into  the  compression  cylinder  has  been 
primitively  raised  to  a  certain  pressure,  say  40  Ibs.;  the  com- 
pression carries  this  pressure  to,  say  160  Ibs.;  then  the  air 
passes  through  the  cooler  into  the  expansion  cylinder,  wherein 
it  again  expands  from  160  Ibs.  to  40  Ibs.  or  more,  according  to 
the  temperature  at  which  it  is  desired  to  discharge  it  through  a 
pipe  like  r;  but  instead  of  being  allowed  to  diffuse  freely  into 
the  cold  storage  ducts  or  chambers,  this  air  is  circulated  through 
coils  of  closed  pipe,  which  are  finally  connected  to  the  inlet 
valve  chamber  of  the  compression  cylinder,  the  same  air  being 
thus  used  over  and  over  again. 

This  machine  operates  upon  a  greater  weight  of  air  under  a 
given  volume,  and  consequently  is  more  effective  under  this 
volume,  than  the  Bell-Coleman  machine.  Or  else,  the  Allen 
machine  can  produce  the  same  cooling  effect  with  smaller 
dimensions  than  the  Bell-Coleman,  which  is  an  important  fea- 
ture on  shipboard. 

It  is  interesting  to  form  an  idea  of  the  practical  results 
which  can  be  attained  with  this  sort  of  machine,  to  which 
object  the  following  data  refers: 

One  pound  of  ice  at  32  degrees  to  be  transformed  into  water 
at  32  degrees,  absorbs  142  B.  T.  U.  without  variation  of  temper- 
ature. 

This  amount  of  heat,  which  disappears,  without  influencing 
the  thermometer's  indications,  is  termed  the  latent  heat  of 
fusion  of  ice.  In  the  same  way,  if  we  want  to  transform  i  Ib. 
of  water  at  32  degrees  Fahr.,  into  ice  at  32  degrees  Fahr.,  we 
must  subtract  142  B.  T.  U.  from  that  pound  of  water,  without 
changing  its  temperature,  and  these  142  B.  T.  U.  are  the  latent 
heat  of  solidification  of  water.  These  two  terms  are  entirely 
equivalent. 

One  ton  of  2000  Ibs.  of  ice  in  the  process  of  melting  into 
water  at  32  degrees  Fahr.,  will  therefore  subtract  from  the  sur- 
rounding bodies,  air,  water,  or  whatever  they  may  be,  2000x142 
or  284,000  B.  T.  U.,  and  the  resulting  effect  produced  on  those 
bodies  is  measured  by  /  ton  of  ice  melting  capacity. 

The  refrigerating  action  of  a  machine  or  process  of  any 
kind,  producing  that  same  effect,  is  estimated  in  the  same 
terms,  and  such  a  machine  is  said  to  have  a  cooling  capacity 
of  i  ton  ice  melting. 

The  annexed  Table  gives  the  numbers  of  negative  B.  T.  U. 
and  of  Ibs.  of  ice  melting  capacity,  developed  in  the  adiabatic 
expansion  of  i  cubic  foot  of  air  from  60,  70,  80,  90,  and  100  Ibs. 
gauge  respectively  to  14.7  Ibs.  absolute;  these  are  the  calculated 
or  theoretical  capacities. 

These  figures  show  that  there  is  no  advantage  in  using  a 
high  air  pressure,  because  the  refrigerating  capacity  does  not 


68 


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COMPRESSED   AIR.  69 

vary  proportionately  with  the  rise  of  pressure;  for  instance,  if 
this  latter  passes  from  60  to  70  Ibs.,  the  pressure  increases  by 
1 6  per  cent  and  the  cooling  capacity  by  9  per  cent;  while  if  the 
pressure  becomes  100  Ibs.  the  increase  of  pressure  is  65  per 
cent  and  the  increase  of  cooling  capacity  is  23  per  cent.  In 
other  words,  the  percentage  of  pressure  having  increased  4.1 
times,  the  percentage  of  cooling  capacity  rises  only  2.5  times. 

No  very  complete  record  of  experiments  has  been  published 
showing  the  practical  efficiency  of  cold  air  machines,  one 
reason  being  that,  for  this  special  object,  their  use  is  limited, 
as  compared  with  the  ammonia  machines.  But  whenever  cold 
air  machines  are  adopted,  it  is  because  their  efficiency  is  super- 
seded by  other  practical  reasons.  Some  accurate  tests  place  it 
at  43  per  cent  of  the  theoretical  cooling  capacity  of  the  air  for 
the  Bell-Coleman,  and  37  per  cent  for  the  Allen  Dense-Air 
Engine. 

The  former  coefficient  has  been  used  to  establish  the  column 
of  the  Table  headed  "Practical  Capacity." 

But  while  in  a  large  city,  where  ammonia  can  be  readily  ob- 
tained a  wholesale  ice-making  and  cold-storage  business  would 
not  be  undertaken  with  a  compressed  air  plant,  it  is  none  the 
less  certain  that  in  mining  camps,  or  in  remote  localities,  where 
cheap  motive  power  is  frequently  obtainable,  the  application  of 
air  to  the  production  of  cold  remains  one  of  the  most  interest- 
ing and  profitable  adjuncts  of  this  valuable  power  agency. 


70 


COMPRESSED   AIR. 


COMPRKSSED   AIR.  71 

POWER   TRANSMISSION   BY   COMPRESSED 
AIR. 

The  use  of  compressed  air  for  transmitting  power  for  a  long 
distance  is  daily  gaining  in  importance,  and  this  application  of 
air,  which  a  few  years  ago  did  not  receive  much  consideration, 
outside  of  actuating  rock  drills  and  coal  cutters,  stands  at  present 
as  one  of  the  most  economical  and  satisfactory  systems  of  power 
transmission. 

No  fair-minded  and  impartial  person  will  contend  that  in 
every  possible  case  in  practise  one  particular  system  of  power 
transmission  can  be  always  preferable  to  all  others. 

The  economical  solution  of  industrial  problems  involves  so 
many  factors  of  entirely  independent,  and  often  contradictory 
nature,  that  the  strictly  engineering  side  of  the  question  may 
be  overcome  in  importance  by  other  conditions  which  would 
hardly  have  been  thought  of  at  a  first  glance. 

One  fact  however,  may  be  stated  as  general,  and  that  is  that 
compressed  air  is  better  adapted  to  underground  work  than  any 
other  agency  of  power  transmission.  Not  only  can  it  be  trans- 
ported anywhere,  through  crooked  and  narrow  passages,  either 
wet  or  dry,  and  regardless  of  insulation  or  losses  other  than 
leakage  at  the  pipe  joints,  but  its  use  and  handling  is  totally 
devoid  of  danger,  and  after  its  work  is  done  it  becomes  the 
most  essential  element  to  human  life.  This  can  be  said  of  air 
alone,  although  it  has  nothing  to  do  with  its  value  as  a  power 
transmitter. 

The  principles  of  the  production  of  compressed  air  are  ex- 
pounded in  another  part  of  this  Treatise;  it  is  therefore  unnec- 
essary to  explain  here,  how,  when  air  has  been  raised  to  a 
certain  pressure,  with  production  of  heat,  and  when  on  its  pas- 
sage through  a  long  pipe,  this  air  has  cooled  down  to  the  tem- 
perature of  the  atmosphere,  the  loss  of  efficiency  incurred  in 
this  drop  of  temperature  can  be  balanced,  and  even  exceeded, 
by  reheating  the  air  before  it  is  admitted  to  the  motors. 

This  reheating,  which  can  be  done  at  a  small  expenditure  of 
fuel,  is  an  important  element  in  the  total  efficiency  of  the 
system. 

Being  now  in  possession  of  all  the  essential  elements  of 
information  required  in  estimating  the  size  and  the  cost  of  a 
compressed  air  transmission,  their  application  to  some  practi- 
cal examples  will  form  a  fitting  conclusion  to  the  preceding 
developments: 

EXAMPLE  i. 

A  stamp  mill  is  located  at  3000  feet  from  a  water  wheel 
developing  70  B.  H.  P. 

Required  a  compressed  air  transmission  to  deliver  40  H.  P. 
on  the  line  shaft. 

The  motor  operating  the  mill  is  500  feet  higher  up  than  the 
air  receiver,  wherein  the  air  pressure  is  to  be  80  Ibs. 


72  COMPRESSED     AIR. 

Altitude  of  compressor:  3500  feet  above  sea  level. 
Temperature  at  compressor  and  Mill,  50  degrees  Fahr. 


The  loss  from  belt-slipping  between  the  cam  shaft  and  the 
motor  shait,  and  from  other  causes,  can  be  taken  as  10  per 
cent,  and  the  I.  H.  P.  of  the  motor  will  be: 

?=44-4 

and  assuming  another  loss  of  8  per  cent  for  clearance,  wire 
drawing,  etc.,  the  available  power  at  the  lower  end  of  the  main 
must  be:  48.3  H.  P. 

As  there  is,  at  first  glance,  an  important  margin  between 
the  powers  at  the  wheel  and  at  the  mill,  it  naturally  occurs  to 
consider  whether  the  reheating  of  the  air  at  the  motor  cannot 
be  dispensed  with. 

We  will  use  a  slide-valve  engine,  cutting  off  at  ^  stroke, 
which  would  likely  be  the  earliest  admissible  cut-off  as  regards 
exhaust  temperature. 

The  amount  of  air  necessary  to  develop  48.3  H.  P.  is:  1.13 
Ibs.  per  second,  or  67.8  Ibs.  per  minute.  If  we  were  at  the  sea 
level,  i  Ib.  of  air  at  60  degrees  Fahr.  would  represent  13.1 
cubic  feet. 

Sixty-seven  and  eight-tenths  pounds  represent,  therefore: 
67.8x13.1=888.2  cubic  feet. 

If  we  use  a  single  stage  compressor,  the  I.  H.  P.  required 
for  80  Ibs.  gauge  receiver  pressure  will  be: 
15.18x8.882=134.83. 

But  the  Table  of  columns  and  powers  at  various  altitudes 
shows  that  the  power  required  to  compress  and  deliver  the 
same  volume  of  air  at  the  same  pressure,  but  at  3500  feet  alti- 
tude, is  (Cols.  5  and  6): 

89xi5372— i-o67  times  greater  than  at  the  sea  level. 
And  as  the  temperature  is  50  degrees  Fahr.,  this  figure  should 
be   reduced  in   the  ratio  of  the   absolute  temperature  (at    60 
degrees  and  50  degrees  Fahr.)  and  becomes  1.046. 

The  power  actually  required  will  therefore  be: 

!34- 83X1. 046=141  I.  H.  P.  in  the  compressor. 
And  if  we  allow  it  mechanical  efficiency,  the  brake  power  on 
the  wheel  is: 

^=155  B.  H.  P. 
Whilst  we  have  only  70  B.  H.  P.  at  our  disposal. 

The  air  cannot  therefore  be  used  cold  in  the  motor;  in  other 
words,  we  have  not  yet  a  sufficient  margin  of  power  between 
the  wheel  and  the  mill  to  permit  the  use  of  cold  air;  reheating 
must  necessarily  be  resorted  to. 

We  have  70  B.  H.  P.  on  the  compressor  shaft,  and  70X0.9= 
63  I.  H.  P.  in  the  air  cylinder. 

From  the  above  calculations,  we  know  that  the  compression 
and  delivery  of  100  cubic  feet  of  free  air  per  minute  at  80  Ibs. 
receiver  pressure,  and  at  the  given  altitude  and  temperature, 
require:  15.18x1.046=15.88  I.  H.  P. 


COMPRESSED   AIR.  73 

The  available  power  of  63  I.  H.  P.  will  permit  of  compress- 
ing i  oox^—397  cubic  feet  of  free  air  per  minute,  whose  weight 
at  3500  feet  altitude  and  50  degrees  Fahr.  is:  s^*$Z& 

o  493 

397X.oto7Xsi^30.97.  (UNIVERSITY 
Giving  per  second  a  weight  of  air  of: 
3-^=5i6  Ibs. 

We  have  next  to  determine  the  air  pressure  at  the  lower  end 
or  outlet  of  the  main,  for  a  length  of  3000  feet. 

The  tables  of  frictioual  resistance  show  that  80  Ibs.  gauge 
(94.7  Ibs.  absolute)  being  the  pressure  at  entrance  to  the  main, 
the  pressure  at  the  lower  end  is: 

With  a  4-inch  main:  77.7  Ibs.  gauge. 

With  a  3-inch  main:  73.  Ibs.  gauge. 

Besides,  as  the  outlet  of  the  main  is  500  feet  above  the  re- 
ceiver, we  lose  from  this  fact  1.7  Ibs.,  which  leaves  as  available 
pressures  at  the  outlet: 

With  a  4-inch  main:  76  Ibs.  gauge. 

With  a  3-iuch  main:  71.3  Ibs.  gauge. 

We  will  use  the  4-inch  main,  and  as  the  necessary  reheating 
obviates  the  low  temperature  of  exhaust  caused  by  a  long 
expansion,  we  will  use  a  motor  expanding  from  76  Ibs.  to  2 
Ibs.  gauge,  and  find  that  to  develop  48.3  H.  P.  with  516  Ibs. 
of  air  per  second,  this  air  must  be  reheated  to  247  degrees  Fahr. 

What  amount  of  fuel  this  reheating  will  require  can  be 
easily  computed. 

We  have  to  reheat  30.97  Ibs.  of  air  per  minute,  from  50 
degrees  to  247  degrees  Fahr.,  or  197  degrees  Fahr. 

The  specific  heat  of  air  being  .238,  this  will  require: 

30.97  X- 238x197=1451-9  B.  T.  U.  per  minute,  or: 

i45i.9Xi44Or=:2.09o736  B.  T.  U.  per  24  hours. 

And  allowing  that  i  Ib.  of  coal  will  yield  10,000  B.  T.  U. 
209  i  Ibs.  of  coal  per  24  hours. 

Or  if  i  Ib.  of  pine  wood  will  yield  5400  B.  T.  U.,  the  weight 
consumed  per  24  hours  is:  309.1% -5-^06=386.84. 

Or  about  %  cord. 

SIZE  OF  COMPRESSOR. 

We  found  as  the  "useful"  amount  of  air  per  minute  397 
cubic  feet,  and  allowing  .85  volumetric  efficency  for  the  com- 
pressor, its  intake  capacity  must  be  467  cubic  feet. 

With  300  feet  per  minute  piston  velocity,  and  referring  to 
Table  (Fig.  37),  the  compressor  will  be  a  single  i8^-inch  ma- 
chine, or  a  duplex  12^ -inch  machine. 

EFFICIENCY  OF  THE  TRANSMISSION. 

The  apparent  efficiency  of  the  transmission  is: 

fan 

But  its  exact  value  should  take  into  account  the  coal  con- 
sumed in  reheating  the  air. 


74  COMPRESSED   AIR. 

This  latter  amounts  to  8.70  Ibs.  per  hour,  and  if  we  assume 
that  in  a  compound  steam  engine  the  coal  consumption  is  2  Ibs. 
per  I.  H.  P.,  this  quantity  represents:  8--°=4.35  I.  H.  P.  on  the 
piston  of  a  direct-acting  steam  engine  operating  the  compressor, 
or,  in  the  present  case,  on  the  compressor  shaft. 

The  true  efficiency  is  therefore: 

74^5—  -54 

With  reverse  conditions,  i.  e.,  mill  500  feet  below  compressor, 
the  total  efficiency  would  be  55. 

This  is  an  example  of  a  comparatively  low  efficiency  in 
transmission.  The  power  is  so  small  that  comparative  losses 
become  large.  This  transmission,  however,  can  be  improved 
by  using  a  2  -stage  compound  compressor  and  motor,  the  calcu- 
lations for  which  would  be  as  follows: 

379  cu.  ft.  of  free  air  at  sea  level,  and  50°  Fahr.  4"  pipe. 

Absolute  pressure  ,  «  g.) 


COMPOUND  MOTOR. 

First  reheating,  50°  to  350°  Fahr. 

Power  in  H.  P.  cylinder  ................   32.84 

Second,  153°  to  350°  Fahr. 

Power  in  L,.  P.  cylinder  .................   27.26 

Total  ................    60.  10 

First  loss,  8  per  cent,  as  in  preceding  example. 

60.  ix-  92=55.  29 
Second  loss,  10  per  cent 

55.  29X.9=  49.76 

on  line  shaft. 

Coal  used  for  reheating:    12.58  Ibs.  per  hour,  corresponding 
to:    6.29  I.  H.  P. 


Total  efficiency:    m**  652 


65.2  per  cent. 


EXAMPLE  2. 

A  system  of  Power  Transmission  will  now  be  considered  in 
the  case  of  a  large  mine,  requiring: 
100  B.  H.  P.  for  hoisting         } 
100  B.  H.  P.  for  pumping        {     .,  ..     surface 
100  B.  H.  P.  for  a  stamp  mill  f  At  t 
25  B.  H.  P.  for  lighting 

And 

25  B.  H.  P.  for  hoisting  "] 

25  B.  H.  P.  for  pumping 

1500  cu.  ft.  of  free  air  per    j-  At  1500  ft.  level, 
minute  at  6p  degrees  Fahr.    | 
for  rock  drills 


COMPRESSED  AIR.  75 

Length  of  Transmission  to  surface  plant:    4  miles. 
Compressors  of  the  2-stage  Compound  type. 
Receiver  pressure  75  Ibs.  gauge. 
Outside  temperature  60  degrees  Fahr. 
Permissible  loss  of  pressure: 

In  surface  main:     i  Ib. 

In  underground:     l/z  Ib. 
Required: 

Size  of  surface  and  underground  mains. 
Size  of  Compressor. 
B.  H.  P.  on  compressor  shaft. 

The  power  received  at  the  mine  will  be  divided  under  two 
heads,  viz:  Surface  and  Underground. 

SURFACE  PLANT. 

We  will  assume  for  the  motors  a  mechanical  efficiency  of  .9, 
giving  -£-=361  H.  P.;  and  then,  another  loss  of  5  per  cent 
between  the  cylinder  and  the  lower  end  of  the  main,  for  wire- 
drawing, elbows,  etc. 

The  available  power  at  the  end  of  main  is: 

361          o» 

^=38o> 

the  total  efficiency  being  .9  X.  95=^855. 

The  absolute  pressure  at  upper  end  of  main  is:    89.7 
The  absolute  pressure  at  lower  end  of  main  is:    88.7 
and  the  weight  of  air  at  this  pressure,  reheated  to  400  degrees 
Fahr.  and  completely  expanded  is:    3.26  Ibs.  per  second. 


UNDERGROUND 

Pressure  at  top  of  main:    88.7 

Pressure  at  bottom  of  main  ............  88.2 

Additional  pressure  at  bottom  of  main,  4.8,  due  to  weight 
of  air. 

Absolute  pressure  at  1500  level  .........  93.0 

Fifty  B.  H.  P.  with  .855  efficiency  give:  58.5  H.  P.,  which 
require  a  weight  of  air  per  second  of:  .59  Ibs. 

The  rock  drills  work  practically  at  full  pressure,  and  the 
expansion  of  19  Ibs.  (to  60  Ibs.  gauge)  cannot  be  utilized. 

The  temperature  of  the  compressed  air  at  the  bottom  of 
shaft  column  is  250  degrees,  and  assuming  a  loss  of  ico  degrees 
before  reaching  the  drills,  i.  e.,  a  temperature  of  150  degrees  at 
the  drills,  the  1500  cubic  feet  of  air  will  have  to  be  reduced  in  the 
ratio  of:  ^,  and  become:  1275  cu.  ft.,  whose  weight  is  (per 
minute)  97.41  Ibs. 

The  total  weight  of  air  to  be  supplied  per  second  is,  there- 
fore: 

Surface:  3.26 

Underground:    .59 
Rock  Drills:     1.62 

Total      5.47  Ibs. 


76  COMPRESSED   AIR. 

corresponding  to  4299.43  cubic  feet  per  minute  of  free  air  at  60 
degrees  Fahr.,  whose  compression,  in  a  2-stage  Compound 
Compressor,  will  require: 

578.8  I.  H.  P. 
With  .9  mechanical  efficiency,  the  B.  H.  P.  is: 

643  B.  H.  P. 

The  reheating  will  require  159.34  Ibs.  of  coal  per  hour,  cor- 
responding to:  67  B.  H.  P.,  making  a  total  B.  H.  P.  of,  710 
B.  H.  P. 

The  power  obtainable  at  the  lower  end  of  main  is: 

637.3  H.  P. 
and  on  the  shaft  of  the  motors,  with  .855  efficiency: 

545  B.  H.  P. 
The  total  actual  efficiency  is,  therefore:  ^=76.7. 

.  SIZE  OF  MAINS. 

The  Tables  of  frictional  resistances,  of  which  the  use  has 
been  explained,  give,  as  proper  size  of  the  pipes: 
For  the  surface  main:     12^  inches. 
For  the  shaft  column:     6-$  inches. 

SIZE   OF  COMPRESSOR. 

The  useful  capacity  has  been  found  as: 

4299.42  cubic  feet  of  free  air  per  minute. 

Taking  for  the  compressor  85  per  cent  volumetric  efficiency, 
the  actual  capacity  is:  5058  cubic  feet,  and  with  400  feet  of 
piston  velocity,  we  will  find  by  referring  to  Fig.  37  the  proper 
size  of  the  compressor. 

It  is  desirable,  for  reasons  of  practical  convenience,  to 
divide  the  compressing  plant  in  two  equal  units,  each  formed 
of  a  duplex  compound  machine.  There  will  be,  consequently, 
4  intake  cylinders,  each  having  a  capacity  of  1264  cubic  feet  per 
minute,  which  correspond  to  a  diameter  of  24^  inches. 

For  75  Ibs.  gauge  receiver  pressure,  the  area  of  the  H.  P. 
cylinder  should  be:  189.36  square  inches,  corresponding  to  15^ 
inch  bore,  and  at  the  rate  of  80  revolutions  per  minute,  the 
stroke  will  be  2  feet,  6  inches.  So  the  size  of  cylinders  is: 


EXAMPLE  3. 

IOO   H.  P.  DELIVERED   BY  WHEEL,    2    MILES,    5-INCH   PIPE. 

REQUIRED:    Potential  at  lower  end  of  line. 
80  Ibs.  gauge  receiver  pressure. 

One  hundred  B.  H.  P.  will  compress  and  deliver  598  cubic 
feet  of  free  air  per  minute,  or  9.95  cubic  feet  of  free  air  per 
second,  corresponding  to:  1.546  cubic  feet  per  second  of  cold 
air  at  80  Ibs.  gauge. 

The  velocity  at  entrance  in  a  5-inch  pipe  is:  11.35  feet  per 
second,  and  the  absolute  pressure  at  the  lower  end  of  the  line 
is  94-7X-  977=92.52  absolute=77.82  gauge. 


COMPRESSED  AIR.  77 

Available  work: 

If  air  is  used  cold    54.6  per  cent. 

If  air  is  reheated  from 

60°  to  300°  Fahr 79. 7  per  cent. 

If  air  is  reheated  from   . 

60°  to  350°  Fahr 84.9  per  cent. 

FUEL  CONSUMPTION 

Reheating  to  300°  Fahr  ...  %  cord  of  wood  in  24  hours. 
Reheating  to  350°  Fahr.  . .  .  >£  cord  of  wood  in  24  hours.  • 

The  total  efficiency,  taking  into  account  the  fuel  consumed, 
is,  plain  expansion,  single  cylinder: 

Cold  Air 54. 6  per  cent. 

Reheating  to  300° 75.9  per  cent. 

Reheating  to  350° ; .   79  per  cent. 

The  total  efficiency,  taking  into  account  the  fuel  consumed, 
using  compound  cylinders  and  reheating  for  both  high  and 
low  pressure  cylinders  is: 

Reheating  to  300° 80.7  per  cent. 

Reheating  to  350° 83.3  per  cent. 

EXAMPLE  4. 
PUMPING  8  MINER'S  INCHES  OF  WATER  500  FEET  HIGH 

WITH   DIRECT-ACTING  PUMP. 

Consumption  of  cold  free  air  per  minute 352  cu.  ft. 

If  air  is  heated  (dry)  from  60°  Fahr.  to  300°  Fahr. 
the  consumption  falls  to    241  cu.  ft. 

FUEL  CONSUMPTION: 

24  r  cu.  ft.=i8  412  Ibs.  air  per  minute, 
i  Ib.  of  air  raised  in  tempera- 
ture by  240°  absorbs 57.12  B.  T.  U.  per  minute. 

3,427.2    B.  T.  U.  per  hour. 
82,252.      B.  T.  U.  per  24  hours. 

and  18.412  Ibs.  will  require.  ..1,513,452.      B.  T.  U.  per  24  hours. 

Assuming  i  Ib.  wood  to  yield  5000  B.  T.  U.,  and  i  cord= 

2000  Ibs.  the  consumption  is:     .153  or  l/&  cord  per  24  hours. 


78  COMPRESSED   AIR. 


AN   EXAMPLE   OF   A   COMPRESSED   AIR   AND   AN 
ELECTRICAL   TRANSMISSION. 

To  be  supplied  at  the  mine: 

100  H.  P.  to  drive  motors  and 

500  cu.  ft.  free  air  per  minute,  compressed  to  80  Ibs. 
The  latter  requires  83.5.  B.  H.  P.     Now,  assuming  a  motor 
efficiency  of  .95  there  will  be  required  at  motor  in  the  electrical 
transmission: 

^=87.8  H.  P 87.8 

100  H.  P.  for  machinery. 

-g-g  at  motor  driving  machinery 105.2 

Power  at  lower  end  of  conductor 193-° 

2  per  cent  loss  on  line. 

193 

Power  at  upper  end  of  line:    ~s=  197 

.95    generator    efficiency   B. 

H.  P.  on  generator:  


207 

AIR   TRANSMISSION. 


500  cu.  ft.  for  drills. 
675  for  100  B.  H.  P. 


1175 
requiring:  n. 75x16.7=196.22  B   H.  P. 


RIX   AIR   COMPRESSORS 


MANUFACTURED   BY  THE 

Fulton  Engineering  and  Shipbuilding  Works 

SAN  FRANCISCO,  CAL. 


RIX  AIR  COMPRESSORS 


MANUFACTURED   BY  THB 


Fulton  Engineering  and  Shipbuilding  Works 

SAN   FRANCISCO,  CAL. 


After  the  preceding  article  on  the  different  phenomena  and 
laws,  both  theoretical  and  practical,  which  enter  into  the  sub- 
ject of  compressed  air  engineering,  it  seems  right  and  proper 
to  set  forth  as  plainly  as  possible  the  different  styles  and  gen- 
eral specifications  of  the  air  compressors  manufactured  espe- 
cially on  this  Pacific  Coast. 

These  compressors  are  all  designed  and  built  under  the 
special  superintendence  of  Mr.  Edward  A.  Rix,  by  the  Fulton 
Engineering  and  Shipbuilding  Works,  and  are  the  result  of 
some  eighteen  years'  experience  in  pneumatics  on  the  Pacific 
Coast. 

There  is  no  doubt  that  from  the  conditions  under  which 
mining  is  carried  on  on  the  Pacific  Coast,  one  would  naturally 
expect  to  see  a  different  style  and  class  of  air  compressor  built 
from  those  manufactured  in  the  East.  The  facilities  for  trans- 
portation are  vastly  different.  The  special  requirement  for 
prospecting  plants,  which  shall  be  cheap  and  easily  operated, 
and  the  tremendous  heads  of  water  which  are  found  on  the 
Pacific  Coast,  necessitate  a  peculiar  construction  of  compressor, 
and  the  large  varieties  manufactured,  descriptions  of  which 
follow  hereafter,  give  the  intending  purchaser  or  operator 
ample  opportunity  to  select  machines  especially  fitted  to  his 
character  of  work. 

All  of  the  Rix  Compressors  are  of  the  water-jacket  type; 
that  is,  the  partial  cooling  during  compression  is  effected  by 
circulating  water  in  a  jacket  around  the  cylinder  and  through- 
out the  heads  of  the  air  cylinder.  Frequently,  also,  this  cir- 
culation is  carried  within  the  r^stons  of  the  machine,  but  no 
water  whatever  is  injected  into  the  cylinder.  This  method  of 
construction  has  been  constantly  followed  ever  since  the  manu- 
facture of  these  machines  was  begun  some  eighteen  years  ago, 
even  though  during  this  time  the  principal  Eastern  manufac- 
turers were  still  enamored  of  the  injection  system. 

This  jacket  circulation  is  not  a  simple  one,  and  in  the  small- 
est of  the  machines  is  double,  that  is,  there  are  two  independent 
water  circulations  for  the  machine,  the  water  entering  the 
lower  part  of  the  cylinder  at  two  openings,  going  thence  im- 
mediately and  independently  to  each  head  and  then  around 


82  RIX    AIR    COMPRESSORS. 

the  body  of  the  cylinder  and  finally  escaping  at  two  inde- 
pendent outlets. 

In  all  cylinders  of  large  diameter  or  for  high  pressure,  the 
heads  are  often  built  with  independent  circulations.  In  this 
manner  cold  water  is  assured  to  many  parts  of  the  cylinder  at 
the  same  time. 

All  of  the  Standard  Rix  Compressors  for  ordinary  use  have 
inlet  valves  of  the  poppet  type,  that  is,  the  valves  have  neither 
nuts  nor  bolts  nor  threads,  and  there  is  nothing  about  them  to 
get  out  of  order,  and  they  cannot  fall  into  the  cylinder.  They 
are  subjected,  of  course,  to  the  visual  wear  and  tear  in  their 
springs,  and  these  may  be  taken  out  in  a  few  seconds  and  re- 
placed as  easily. 

The  outlet  valves  of  the  standard  machines  are  of  the  check 
valve  type,  well  known  to  most  all  builders  of  compressed  air 
machinery. 

The  frames  are  made  in  two  general  styles,  one  of  the  Cor- 
liss pattern,  and  the  other  of  flat  bed  pattern  with  slipper  cross 
head,  one  being  designed  for  heavy  and  one  for  light  duty. 

All  of  the  working  parts,  such  as  cranks,  boxes,  shafts,  pis- 
tons, etc.,  are  made  in  conformity  with  the  best  engineering 
practise.  The  crank  pins  specially  are  made  unusually  large, 
so  that  they  do  not  heat  with  the  intermittent  work  which  is 
placed  upon  them. 

The  water  jackets  can  be  readily  cleared  out  of  any  mud  or 
sediment  which  may  form  therein,  inasmuch  as  when  the  heads 
are  taken  off  the  jackets  are  completely  exposed.  This  is  a 
very  convenient  device. 

Sight  feed  lubricators  and  all  necessary  oilers  and  standard 
fittings  are  furnished  with  every  machine. 

In  the  tables  for  the  various  compressors  there  have  been 
no  capacities  mentioned  for  cubic  feet  of  free  air.  Inas- 
much as  the  cubic  feet  of  free  air  will  depend  entirely  upon 
the  piston  speed  of  the  machine  and  inasmuch  as  the  piston 
speed  of  the  machine  depends  to  a  great  extent  upon  a  number 
of  circumstances,  it  is  deemed  easier  to  use  the  following  table 
to  determine  the  capacities  of  any  of  the  compressors.  It  will 
be  noted  that  the  left-hand  column  contains  the  cylinder 
diameters  of  the  various  sized  compressors  manufactured  by 
the  Fulton  Engineering  Company,  and  on  the  right  of  this 
column,  under  the  piston  speeds  mentioned,  will  be  found  the 
various  capacities  for  these  Cylinders,  at  the  piston  speeds 
directly  above. 

From  this  table  it  will  be  easy  to  select  the  proper  size  of 
compressor  to  do  the  work  required,  for  all  the  tables  in  this 
treatise  give  the  number  of  cubic  feet  of  air  required  to  do  the 
various  kinds  of  work.  It  will  only  be  necessary  then  to  find 
the  total  number  of  cubic  feet  required  and  to  select  the  piston 
speed  most  advantageous  to  at  once  determine  the  proper  size 
of  cylinder.  For  example,  from  the  requirements  if  it  has  been 
determined  that  350  feet  of  piston  velocity  per  minute  is  as 
much  as  is  desirable  and  that  the  cubic  feet  of  air  required  is 


RIX   AIR  COMPRESSORS.  83 

about  550  cubic  feet  per  minute,  then  an  i8%-inch  cylinder 
would  be  the  proper  size  for  a  single  compressor,  or  a  duplex 
14^,  making  somewhat  less  than  300  feet  of  piston  velocity 
minute. 

The  question  of  determining  the  piston  velocity  is  one  of 
the  vital  points  in  the  selection  of  an  air  compressor.  Notwith- 
standing anything  which  may  be  said  to  the  contrary,  the  most 
economical  compressor  is  one  which  moves  at  a  slow  piston 
velocity  and  high  piston  velocities  are  only  used  to  save  initial 
expenditure.  Therefore,  when  one  contemplates  the  install- 
ment of  a  permanent  air  compressing  plant  or  one  which  will 
likely  be  operated  for  one  or  more  years,  it  is  always  better  to 
select  a  low  piston  speed  and  pay  the  extra  price  for  the  larger 
machine  which  this  entails,  than  to  pay  the  extra  fuel  bill 
caused  by  a  higher  velocity. 

It  is  to  be  regretted  that  most  purchasers  do  not  understand 
the  value  of  a  low  piston  speed  for  an  air  compressor.  A  low 
initial  price  seems  to  be  the  principal  virtue.  There  is  not 
room  enough  in  the  ordinary  cylinder  diameter  to  give  the 
proper  ingress  and  egress  of  air  under  economical  conditions. 
An  indicator  card  from  most  compressors,  running  under  a 
piston  speed  of  400  feet  per  minute,  shows  an  enormous  increase 
of  pressure  to  force  the  air  through  the  delivery  valves, 
which,  of  course  means  a  corresponding  loss.  The  ideal  indi- 
cator card  is  one  which  shows  no  suction  pressure,  and  which 
shows  that  the  delivery  valves  open  at,  or  nearly  at,  the  receiver 
pressure.  Practically,  this  is  not  accomplished,  and  there  are 
few,  if  any ,  compressor-builders  proud  of  the  indicator  card  taken 
from  one  of  their  compressing  cylinders  at  such  a  piston  speed. 
Yet  their  machines  are  forced  to  such  speeds,  oftener  constantly 
than  frequently.  The  writer  has  taken  cards  from  various 
machines  that  showed  10  per  cent  of  power  used  in  forcing  air 
through  the  delivery  valves.  It  is  not  a  simple  matter  to 
make  a  practical  machine  that  shall  work  economically  at 
high  piston  speed.  It  is  at  present  far  better  practise  to  use  a 
compressor  at  low  piston  speed  and  avoid  those  losses  which 
cannot  be  recovered.  The  ideal  system  of  compression  is  a 
continuous  one,  and  while  it  seems  almost  impossible,  the 
writer  has  already  built  one  machine  which  gives  fair  promise, 
and  future  experiments  will  probably  develop  the  question.  In 
continuous  compression  there  are  no  mechanical  cylinder  losses 
that  amount  to  much. 

No  compressor  builder  advocates  high  rotative  or  piston 
speed,  and  for  the  advancement  of  compressed  air  practise  it  is 
to  be  hoped  that  purchasers  will  consult  operative  expense 
rather  than  initial  expenditure. 


84 


RIX   AIR   COMPRESSORS. 


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RIX   AIR   COMPRESSORS. 


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86 


RIX   AIR   COMPRESSORS. 


RIX  DUPLEX  STEAM  ACTUATED 
COMPRESSOR. 

CLASS  A,  FIG.  32. 

Fig.  32  is  a  half-tone  of  the  Rix  Duplex  Steam  Actuated  Com- 
pressor, of  the  flat  bed  type,  having  slipper  cross  head. 

Eig*  33  is  a  plan  °f  this  same  machine,  showing  arrange- 
ments of  foundation  bolts  and  piping. 

Fig.  34  is  an  end  elevation  of  the  same  compressor. 

Fig.  35  is  a  side  elevation  of  the  same  compressor,  and  is  at 
the  same  time  a  side  elevation  of  the  Single  steam  actuated 
compressor. 

Wherever  possible,  it  is  desirable  to  install  a  Duplex  Air 
Compressor.  The  cranks  being  placed  at  right  angles,  the  air 
is  discharged  more  continuously  throughout  the  whole  revolu- 
tion, and  the  result  is  that  the  strains  in  the  machine  are  more 
evenly  divided  and  the  machine  as  a  whole  gives  better  satis- 
faction. 

Another  reason  which  should  prompt  a  Duplex  machine  is, 
that  should  it  be  necessary  to  discontinue  the  use  of  one-half 
of  the  machine  for  repairs,  the  other  half  is  always  available 
and  is  a  complete  working  compressor  in  itself. 

The  following  is  a  table  of  dimensions  for  these  compressors: 

RIX  DUPLEX  STEAM  ACTUATED  COMPRESSOR. 

CLASS   A. 

For  Revolutions  per  minute,  Cubic  Feet  Free  Air,  Rock 
Drill  Capacity,  see  pages  84  and  85. 


No. 

Diameter 
Steam   Cylinder. 

Diameter 
Air  Cylinder. 

Stroke. 

H.     P. 

Boiler. 

Price. 

I 
2 
1 

IO 
12 
14 

10  # 

12^ 
'4>2 

14 
16 
18 

60 
80 
1  10 

16 

i6# 

18 

I4O 

18 

i&lA 

24 

2OO 

6 

7 

20 
22 

20/2 
22/^ 

24 
3° 

2    O 
3IO 

8 

2/1 

2/1  14 

•2Q 

4OO 

RIX   AIR  COMPRESSORS. 


88 


RIX  AIR  COMPRESSORS. 


RTX    AIR    COMPRESSORS. 


89 


FinioN 


ENGINEERING  f  SHIP  BUI IDI NG  WpRl 

i. — 4 -4n  ill 

i  it* 


Fio.  34— Class  A.— Rix  Duplex  Steam  Actuated  Compressor. 


9o 


RTX   AIR   COMPRESSORS. 


RIX   AIR   COMPRESSORS. 


RIX  SINGLE  STEAM  ACTUATED 
COMPRESSOR. 

CLASS  B,  FIG.  36. 

The  following  half- tone,  Fig.  36,  shows  the  general  style  of 
construction  of  Class  B,  Rix  Single  Steam  Actuated  Compressor, 
and  Fig.  35  shows  the  side  elevation  of  same. 

This  machine  differs  only  from  the  Duplex  Compressor  in 
the  fact  that  it  is  one-half  of  that  machine  and  has  an  outboard 
bearing. 

The  following  is  a  table  of  the  various  and  proper 

dimensions. 

RIX  SINGLE  STEAM  ACTUATED  COMPRESSOR. 
CLASS  B. 

For  Revolutions  per  minute,  Cubic  Feet  Free  Air,  and  Rock 
Drill  Capacity,  see  pages  84  and  85. 


No. 

Diameter. 
Steam  Cylinder 

Diameter 
Air  Cylinder. 

Stroke. 

H    P. 
Boiler 

Price. 

IO 

101A 

14 

JQ 

10 

12 

I2>£ 

16 

4O 

II 

14 

14^ 

18 

55 

. 

12 

16 

l6>2 

18 

7O 

13 
14 

18 

2J 

i8# 

2C)>< 

24 
24 

100 

130 



15 

22 

22^ 

3° 

155 

16 

24 

24  K 

30 

2OO 

RIX   AIR   COMPRESSORS. 


RIX  AIR  COMPRESSORS. 


93 


RIX   SINGLE   STEAM   ACTUATED 

COMPRESSOR,  SELF-CON- 

TAINED   TYPE. 

CLASS  C,  FIG.  38. 

This  machine  is  one  which  is  offered  to  the  mining  public  as 
theleast  expensive  andmost  generally  useful  machine  of  the  kind 
ever  constructed.  It  will  be  noted  from  the  half  tone  that  this 
consists  of  an  independent  standard  engine  on  a  bed-plate  con- 
nected to  an  air-compressing  cylinder,  the  whole  being  tied 
together  for  proper  operation.  The  engine  is  self  contained, 
there  being  no  outboard  box,  the  fly  wheel  pulley  being  over- 
hung, so  that  this  machine  can  be  placed  anywhere  and  is 
ready  for  operation  at  once.  A  belt  can  be  placed  upon  the 
fly  wheel  pulley  and  be  used  to  operate  a  pump  or  any  other 
machine  that  may  be  desired  while  the  compressor  is  not  in 
use,  in  which  case  it  will  only  be  necessary  to  remove  one  inlet 
valve  on  each  end  of  the  air  cylinder  and  the  compressor  end 
of  the  machine  becomes  inactive. 

This  machine  is  especially  built  for  prospecting,  temporary 
work  and  for  experiments,  where  a  permanent  plant  is  too 
expensive.  It  will  be  noted,  from  the  construction,  that  the 
engine  can  be  entirely  removed  and  used  independently  should 
occasion  demand,  and  the  whole  arrangement  is  one  which 
gives  a  prospector  an  opportunity  to  easily  dispose  of  his 
machine  should  his  mining  venture  prove  a  poor  one. 

The  following  is  the  list  of  sizes  of  the  Class  C  Compressor. 

RIX  SINGLE  STEAM  ACTUATED  COMPRESSOR,  SELF- 
CONTAINED. 

CLASS  C. 

For  Revolutions  per  minute,  Cubic  Feet  Free  Air,  and  Rock 
Drill  Capacity,  see  pages  84  and  85. 


No. 

Diameter 
Steam  Cylinder 

Diameter 
Air  Cylinder 

Stroke. 

H.  P. 
Boiler            Pnce 

*7 

7 

8 

10 

15             

T8 

8 

8 

10 

2O            .... 

19 

9 

IU^ 

12 

25             .... 

20 
21 

10 
10 

10/2 
Hl/2 

12 
14 

30            
30              

22 

II 

nlA 

14 

^5 

23 

12 

12^ 

16 

4° 

24 

T3 

I2# 

1.6 

4S 

25 

!4 

*4/4 

18 

ss 

26 

16 

ibl/2 

20 

7O 

27 

18 

18/2 

22 

IOO 

f 

94 


R1X    AIR    COMPRKSSORS. 


R1X   AIR   COMPRESSORS. 


95 


RIX    DUPLEX    SHAFT- DRIVEN    COM- 
PRESSOR. 

CLASS  D,  FIG.  39. 

This  half-tone  represents  one  of  the  new  style  Shaft-Driven 
Rix  Duplex  Compressors,  heavy  duty  style.  This  machine  has 
Corliss  frame,  extra  large  wrist  pins,  and  large  cross  head. 
The  frame  is  swelled  up  on  the  front  head  so  that  the  head 
may  be  removed  without  disconnecting  the  cylinder.  The 
Compressor  which  was  the  subject  for  this  half-tone  was  driven 
by  a  twelve-foot  tangential  water  wheel,  under  a  head  of  two 
hundred  and  seventy-five  feet.  It  may,  however,  be  driven  by 
belt. 

Fig.  40  is  a  side  elevation  of  the  same  machine,  showing 
belt  pulley. 

Fig.  41  shows  a  sectional  machine  of  the  same  class,  but 
having  a  flat  bed,  with  water  wheel  attached  upon  the  shaft. 

This  Compressor,  as  all  the  sectional  compressors  herein- 
after mentioned,  is  made  in  sections  not  to  exceed  325  Ibs.  in 
weight,  so  that  they  may  be  carried  upon  mules. 

The  following  table  gives  the  sizes  and  principal  dimen- 
sions for  the  Class  D  machines: 

RIX   DUPLEX   SHAFT-DRIVEN   COMPRESSORS, 

CLASS   D. 

For  Revolutions  per  minute,  Cubic  Feet  Free  Air,  and  Rock 
Drill  Capacity,  see  pages  84  and  85. 


No. 

Diameter 
Air  Cylinder. 

Stroke. 

Price. 

28 

8 

I  2 

2Q 

10% 

14 

T.Q 

17 

16 

11 

MK 

18 

32 
1^ 

16/2 

I&/2 

18 
24. 

201A 

24 

1.Z 

221A 

?o 

^6 

'    2A1A 

10 

96 


RXI   AIR   COMPRESSORS. 


RIX    AIR    COMPRESSORS. 


97 


98 


RTX   AIR    COMPRESSORS. 


RIX   AIR   COMPRESSORS. 


99 


cr 


RIX    DUPLEX   TANDEM    SECTIONAL 
SHAFT-DRIVEN    COMPRESSORS. 

CI,ASS  E,  FIG.  42. 

These  Compressors  are  entirely  similar  to  the  Class  D  Ma- 
chines as  noted  in  Fig.  41,  with  the  exception  that  the  bed 
is  extended  and  an  additional  air  cylinder  placed  tandem  to 
the  others.  This  makes  a  very  convenient  form  of  machine> 
and  one  which  gives  a  large  air  capacity  with  little  additional 
weight.  These  air  cylinders  are  so  connected  up  that  any  one 
of  the  four  cylinders,  or  any  combination  of  the  four  cylinders, 
may  be  run  together.  The  utility  of  this  machine  will  be 
recognized  at  once. 

Fig.  43  is  a  side  elevation  of  this  Class  E  machine. 


RIX    DUPLEX   TANDEM    SECTIONAL    SHAFT-DRIVEN 
COMPRESSORS. 

ClyASS  K. 

For  Revolutions  per  minute.  Cubic  Feet  Free  Air,  and  Rock 
Drill  Capacity,  see  pages  84  and  85. 


No. 

Diameter 
Air  Cylinder. 

No.  of  Air 
Cylinders. 

Stroke. 

Price. 

M 

8 

4 

12 

*8 

iolA 

4 

14 

^Q 

12)4 

4 

16 

4° 

IA]4. 

4 

18 

RIX   AIR   COMPRESSORS. 


bfl 

C 

W 


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X 

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RIX    AIR   COMPRESSORS. 


101 


_r  _  L.  k/'      xj. 


102  RIX  AIR    COMPRESSORS. 

RIX  SINGLE  SHAFT-DRIVEN 
COMPRESSOR. 

CLASS  F,  FIG.  44. 

This  half-tone  shows  a  flat  bed  type  of  compressor,  but  they 
are  made  also  with  Corliss  frames,  as  shown  in  the  Class  D 
machines,  Fig.  40,  the  smaller  machines  being  made  as  per 
Fig.  44.  This  machine  has  an  outboard  bearing  and  may  be 
driven  either  by  belt,  pulley,  or  by  water  wheel  uporAhe  shaft. 

Fig.  45  shows  a  side  elevation  of  this  Class  F  compressor. 

The  following  is  a  table  of  the  sizes  and  general  dimensions 
of  this  style  of  air  compressor: 

RIX  SINGLE  SHAFT-DRIVEN   COMPRESSOR. 

CLASS  F. 

For  Revolutions  per  minute,  Cubic  Feet  Free  Air,  and  Rock 
Drill  capacity,  see  pages  84  and  85. 


No 

Diameter 
Air  Cylinder. 

Stroke. 

Price. 

dl 

8 

I  2 

A2 

I0l4 

Id 

4-2 

l^ 

16 

Ad 

14^ 

18 

AC 

i6}£ 

18 

4.6 

i8# 

21 

A1 

2OT^7 

2A 

48 

"21/ 

-2Q 

dQ 

24  14 

?o 

RIX   AIR   COMPRESSORS. 


104 


RTX  AIR   COMPRESSOR 


RIX   AIR  COMPRESSORS. 


105 


RIX   COMBINED    DUPLEX   STEAM 
ACTUATED    AND    SHAFT- 
DRIVEN  COMPRESSOR. 

CXASS  G,  FIG.  46-46^. 

This  is  a  form  of  compressor  which  is  especially  adapted  to 
the  wants  of  the  Pacific  Coast,  where  there  is  abundance  of 
water  supply  during  one  portion  of  the  season  and  an  insuffi- 
cient supply  during  the  remainder.  It  becomes,  therefore, 
necessary  to  run  the  compressor  with  water  power  during  a 
portion  of  the  year,  and  steam  power  during  the  balance. 

It  will  be  noted  from  the  half  tone  that  the  air  cylinders 
are  placed  next  to  the  water  wheel,  which  water  wheel  has 
been  built  upon  the  fly  wheel  of  the  machine,  the  steam 
cylinders  being  tandem  to  the  air  cylinders,  with  a  sleeve 
coupling  between.  When  it  is  desired  to  run  by  water  power 
it  is  only  necessary  to  remove  the  sleeve  coupling,  and  the 
machine  becomes  a  water  power  compressor.  The  couplings 
may  be  replaced  in  an  hour,  at  any  time,  and  the  machine 
again  converted  into  a  duplex  steam  machine,  using  the  com- 
bined fly  wheel  and  water  wheel  for  a  fly  wheel. 

These  compressors  are  made  in  the  following  sizes: 

RIX    COMBINED     DUPLEX    STEAM    ACTUATED    AND 
SHAFT-DRIVEN   COMPRESSOR. 

CI.ASS   G. 

For  Revolutions  per  minute,  Cubic  Feet  Free  Air,  and  Rock 
Drill  Capacity,  see  pages  84  and  85. 


No. 

Diameter 
Steam   Cylinder 

Diameter          ctrntf 
Air  Cylinder  \ 

H.  P. 
Boiler 

Price 

IO 

iQ/4             14 

60 

51 

12 

12)4                     l6 

80 

52 

14 

14)4              18 

no 

16 

i6lA               18 

I4O 

54 

18 

i8>£               24 

200 

55 

20 

20^               24 

260 

06 

22 

22j^                     30 

"UO 

2A. 

4/2                          30 

4OO 

io6 


RIX   AIR   COMPRESSORS. 


S-l 


K 
6 


RIX   AIR   COMPRESSORS. 


107 


u, 
>> 


I 

a 


I! 


d 


u 


108  RIX   AIR   COMPRESSORS. 


RIX  STEAM  ACTUATED  VERTICAL 
COMPRESSORS. 

CI,ASS  H,  FIG.  47. 

This  style  of  compressor  is  one  which  has  given  universal 
satisfaction  in  this  State,  a  machine  of  similar  type  having  run 
continuously  from  1880  to  the  present  date  with  no  expense 
whatever  beyond  valve  springs.  It  is  single  acting^  the  air 
cranks  being  placed  at  180  degrees  from  each  other,  which 
balances  the  machine  completely,  and  the  cylinders  being  ver- 
tical there  is  no  internal  wear  of  any  consequence.  The  steam 
engine  is  placed  horizontally  on  the  floor,  for  the  double  pur- 
pose of  keeping  the  warmth  of  the  steam  cylinder  away  from 
the  inlet  air,  and  also  for  the  purpose  of  making  the  steam 
crank  at  right  angles  to  the  air  cranks. 

This  compressor  is  made  in  only  one  size:  1 2-inch  steam 
cylinders,  12^-inch  air  cylinders  by  i6-inch  stroke,  and 
catalogued  No.  58.  Capacity  in  free  air  per  minute,  see  page 
84,  both  cylinders  being  the  equivalent  of  one  double-acting 
12^-inch  cylinder,  as  per  table. 

Figs.  48,  49,  and  50  show  different  views  of  this  same 
machine. 


RIX   AIR   COMPRESSORS. 


I09 


\ 


FIG.  47— Class  H.— Rix  Steam  Actuated  Vertical    Compressor.     Manufactured 
by  Fulton  Engineering  and  Shipbuilding  Works,  San  Francisco. 


AS. 

OF  THE  '       \ 

JNIVERSITY) 

IA'  ^ 


no 


RIX   AIR   COMPRESSORS. 


Fici.  48 — Class  H. — Rix  Steam  Actuated  Vertical  Compressor.     Manufactured  by 
Fulton  Engineering  and  Shipbuilding  Works,  San  Francisco. 


RIX   AIR   COMPRESSORS. 


Ill 


« 


Fi  ;.  49— Class  H.—Rix  Steam  Actuated  Vertical  Compressor.    Manufactured 
by  Fulton  Engineering  and  Shipbuilding  Works,  San  Francisco. 


RIX   AIR   COMPRESSORS. 


FIG.    50— Class  H.— Rix  Steam  Actuated  Vertical    Compressor, 
factured  by  FuJton  Engineering  and  Shipbuilding  Works, 
San  Francisco. 


RIX   AIR    COMPRESSORS. 


RIX   SINGLE   CORLISS    ACTUATED 
COMPRESSORS. 

CLASS  I,  FIG  51. 

These  Compressors  consist  of  a  Standard  Corliss  engine,  to 
which  there  is  placed  tandem  the  air  cylinder. 

Fig.  52  shows  a  plan  of  the  single  machine.  They  are  an 
economical  and  high-class  machine  in  every  respect. 

The  following  table  shows  the  sizes  and  dimensions  of  the 
Class  I,  Rix  Single  Corliss  Actuated  Compressors: 

RIX  SINGLE   CORLISS   ACTUATED   COMPRESSORS. 

CLASS  I. 

For  Revolutions  per  minute,  Capacity  Free  Air,  Rock  Drill 
Capacity,  see  pages  84  and  85. 


No. 

Diameter 
St'm  Cylinder, 

Diameter 
Air  Cylinder. 

Stroke. 

Price. 

59 

12 

I2l/2 

3° 

60 

12 

IA*4 

3° 

61 

IAI< 

^O 

62 

14 

iblA 

3° 

61 

16 

r6# 

^o 

64 

16 

iS# 

3° 

65 

16 

16^ 

36 

66 

16 

i&A 

^6 

67 

16 

\6y, 

42 

68 

16 

l§l/2 

42 

69 

18 

18% 

36 

70 

18 

20*4 

^6 

71 

18 

l%l/2 

42 

72 

18 

2O^ 

42 

7* 

18 

i&lA 

48 

74 

iS 

20^ 

48 

114 


RIX   AIR   COMPRESSORS. 


RTX   AIR   COMPRESSORS. 


n6 


RIX   AIR   COMPRESSORS. 


RIX  COMPOUND  CORLISS  ACTUATED 
COMPRESSORS. 

Class  J  comprises  the  Rix  Compound  Corliss  Actuated  Com- 
pressors, which  are  entirely  similar  to  those  of  Class  I  excepting 
that  the  steam  cylinders  are  compound,  the  air  cylinders  being 
alike. 

The  following  is  a  table  showing  the  sizes  and  principal 
dimensions  of  the  Class  J  Compressors: 

RIX  COMPOUND  CORLISS  ACTUATED  COMPRESSORS. 

CLASS  J. 

For  Revolutions  per  minute,  Cubic  Feet  Free  Air,  Rock 
Drill  Capacity,  see  pages  84  and  85. 


No. 

Diameter  High 
Pressure. 

Diameter  I,ow 
Pressure. 

Diameter  Air 
Cylinder. 

Stroke. 

Price. 

75 

12 

22 

12^ 

3° 

76 

12 

22 

14/4 

^O 

77 

14 

26 

14^ 

^O 

78 

14 

26 

i6>^ 

3° 

79 

16 

3° 

i6>£ 

3° 

80 

16 

3° 

18^ 

^o 

81 

16 

3° 

i6K 

16 

82 

16 

3O 

i8lA 

36 

8^ 

16 

7.Q 

16% 

A2 

84 

16 

T.Q 

i8/4 

42 

8s 

18 

T.A 

18% 

^6 

86 

18 

34 

2O1A 

16 

87 

18 

34 

iS*A 

42 

88 
89 

18 
18 

34 
34 

20l/2 
&% 

42 
48 

QO 

18 

34 

20  1A 

48 

Both  the  Compressors  Class  I  or  Class  J  are  furnished  either 
condensing  or  non-condensing. 


RIX  AIR   COMPRESSORS.  117 


RIX   LIGHT  DUTY   COMPRESSOR  OR 
VACUUM   PUMP. 

CLASS  K,  FIG  53. 

This  Compressor  is  adapted  for  very  light  work  and  is  a 
self-coutained  machine  working  from  a  Scotch  yoke.  It  is 
intended  for  pressures  up  to  25  Ibs.  only,  and  can  be  either 
used  as  a  compressor  or  a  vacuum  pump,  the  valves  being 
arranged  for  that  purpose.  It  is  single  acting  and  the  dis- 
charge is  absolutely  complete,  there  being  no  clearance  what- 
ever. It  is  capable  of  creating  a  2g-inch  vacuum. 

Made  in  four  sizes  having  4'',  5",  6",  and  7/x  diameter  of 
cylinders,  and  catalogued  No.  91,  92,  93,  and  94  respectively. 

This  machine  is  a  very  inexpensive  and  satisfactory  com- 
pressor to  have  in  laboratories,  shops,  and  canneries,  or  for 
blowing  crude  oil  into  furnaces.  A  four-inch  belt  is  ample  to 
run  any  of  them.  The  peculiar  feature  which  is  advantageous 
as  a  vacuum  pump  is  the  discharge  valve  which  covers  the 
whole  end  of  the  cylinder.  The  piston  touches  it,  moves  it 
slightly  from  its  seat,  thus  dispelling  all  the  air,  the  valve 
reseating  as  the  piston  begins  the  return  stroke. 


RIX   AIR   COMPRESSORS. 


FIG.  53 — Class  K. — Rix  lyight  Duty  Compressor  or  Vacuum  Pump. 


RIX   AIR   COMPRESSORS.  119 


RIX  STEAM  ACTUATED  DUPLEX 
COMPRESSORS. 

CLASS  L,. 

These  compressors  are  designed  for  compressing  air  to  not 
exceeding  twenty-five  pounds  per  square  inch,  with  a  steam 
pressure  at  from  sixty  to  ninety  pounds.  They  are  made  with 
Scotch  Yoke,  as  may  be  seen  from  the  cut  in  Fig.  54,  and  are 
self  contained  in  every  respect.  They  are  especially  adapted 
for  this  Coast,  for  furnishing  air  for  burning  crude  petroleum 
or  distillate. 

These  machines  are  far  heavier  and  stronger  than  any 
machine  which  is  built  in  the  Hast  for  the  same  purpose;  the 
same  comparative  cylinder  sizes  being  made  about  twenty-five 
per  cent  heavier,  so  that  for  use  on  shipboard  they  may  be 
absolutely  relied  upon  not  to  break  or  give  out  when  at  service. 

These  machines  are  complete  with  all  lubricators,  valves, 
and  also  automatic  governor,  which  will  regulate  the  machine 
to  within  two  or  three  pounds  of  the  receiver  pressure. 

Bach  one  of  these  compressors  is  set  up  in  the  shop  and 
thoroughly  tested  before  shipment,  so  that  the  machine  will  be 
ready  to  go  to  work  as  soon  as  set  upon  its  foundations. 

The  following  are  the  sizes  of  the  Rix  Steam  Actuated  Duplex 
Compressors,  Class  L  : 


R1X  AIR  COMPRESSORS. 


RIX   ATR   COMPRESSORS.  121 


RIX  STEAM  ACTUATED  SINGLE  AIR 
COMPRESSORS. 

CLASS  M. 

These  machines  are  precisely  like  those  of  Class  L,  except- 
ing that  they  are  Single  instead  of  Duplex,  and  are  fitted  up  in 
precisely  the  same  manner. 

They  are  complete  with  governor,  lubricators,  oilers,  and 
wipers. 

Bach  machine  is  tested  before  leaving  the  shop,  so  that  it  is 
ready  for  work  immediately  it  is  erected  upon  its  foundations. 

The  following  are  the  sizes  of  the  Rix  Steam  Actuated  Single 
Air  Compressors,  Class  M: 


122 


RIX   AIR   COMPRESSORS. 


3 

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CO 

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RIX   AIR   COMPRESSORS. 


£3E     -lKnA,. 


123 


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RIX   AIR    COMPRESSORS. 


CLASS  N,  FIG.  54— Duplex  Direct  Acting  vSteam   Actuated  Compressors. 

DUPLEX    DIRECT    ACTING    STEAM 
ACTUATED   COMPRESSORS. 

CLASS  N. 

It  will  be  noted  from  the  cut,  Figure  54,  that  these  com- 
pressors are  made  after  the  style  of  the  DIRECT  ACTING 
STHAM  PUMP,  and  they  are  designed  to  meet  certain  require" 
ments  where  light  pressures  and  inexpensive  or  temporary 
machinery  are  desired.  They  are  the  least  expensive  of  all  com- 
pressors which  are  built,  and  while  they  do  not  have  a  very 
high  volumetric  efficiency,  they  are  easily  installed  and  for  cer- 
tain classes  of  work  are  amply  economical. 

The  AIR  CYLINDERS  are  composition  lined  and  the  PIS- 
TON rods  are  of  brass.  Every  machine  is  fitted  complete  with 
its  PROPER  LUBRICATOR  and  wrenches.  The  VALVE 
MECHANISM  is  so  arranged  that  the  air  pistons  work  against 
a  constant  pressure  at  all  times,  thus  obtaining  quite  a  high 
efficiency  for  this  character  of  compressor,  and  insuring  a  uni- 
form stroke. 

There  are  no  DEAD  CENTERS  on  the  machine,  and  the 
pump  is  consequently  always  ready  to  start.  The  dispensing 
of  the  crank  and  flywheel  renders  it  possible  to  place  this  com- 
pressor in  an  extremely  small  space. 


RIX   AIR   COMPRESSORS.  125 

The  VALVES  in  the  steam  end  are  slide  valves,  and  in  the 
air  and  poppet  valves  of  the  ordinary  type  positively  con- 
trolled by  the  valve  mechanism.  The  entire  apparatus  is  com- 
pact, durable,  and  self-contained.  There  are  no  intricate 
working  parts  whatever,  and  it  requires  very  little  attention 
to  operate  it. 

As  a  general  rule  it  is  desirable  to  operate  this  machine  in 
connection  with  a  PRESSURE  REGULATOR,  which  we  fur- 
nish with  the  machine  if  desired.  The  PRESSURE  REGU- 
LATOR automatically  controls  the  speed,  slowing  down  and 
finally  stopping  the  pump  when  the  desired  air  pressure  is  ob- 
tained, and  gradually  starting  up  again  when  the  air  is  ex- 
hausted from  the  reservoir.  This  regulator  practically  makes 
the  machine  automatic  in  its  operation. 

This  Compressor  is  used  in  BREWERIES  for  BEER 
RACKING,  and  is  especially  desirable  for  that  purpose.  It  is 
also  used  in  running  PNEUMATIC  TOOLS  for  cutting  mar- 
ble or  granite,  or  other  building  stone,  and  also  for  CHIPPING 
and  CALKING  BOILERS;  for  the  running  of  SAND  BLASTS; 
for  the  handling  of  ACIDS  in  refineries;  for  running  small 
PNEUMATIC  CRANES;  for  use  in  RUBBER  FACTORIES, 
or  for  pumping  pressures  upon  AUTOMATIC  FIRE  EXTIN- 
GUISHERS; for  CLEANING  CARS  where  a  jet  of  air  is  used 
to  dust  off  cushions  it  is  especially  valuable  as  an  inexpensive 
and  cheap  machine;  for  the  running  of  CLIPPING  MA- 
CHINES, or  for  running  COAL  CONVEYORS,  or  SMALL 
ROCK  DRILLS,  where  pressures  not  exceeding  fifty  or  sixty 
pounds  are  required;  for  PNEUMATIC  EJECTORS,  or  for 
producing  vacuums  for  FILTERING  purposes;  and  the  enum- 
erable requirements  where  low  pressure  compressed  air  is 
desired. 

For  RUNNING  ROCK  DRILLS  we  do  not  advocate  it  for 
a  permanent  plant,  but  for  a  prospecting  plant  for  small  drills, 
these  compressors  can  be  readily  installed  and  will  prove  first- 
class  in  their  operation. 

These  Compressors  are  particularly  adapted  for  furnishing 
the  compressed  air  to  BURN  PETROLEUM  COMPOUNDS 
UNDER  BOILERS  FOR  GENERATING  STEAM. 


126 


RIX  AIR   COMPRESSORS. 


DUPLEX  DIRECT  ACTING  COM- 
PRESSORS. 

CLASS  N. 

Capacities  calculated  on  piston  speed  of  60  feet  and  volu- 
metric efficiency  of  70  per  cent. 


No. 

Diameter 
of  Steam 
Cylinder. 

Diameter 
of  Air 
Cylinder. 

Stroke. 

Cubic  Feet 
of 
Free  Air. 

<u  S  v 
£&& 

to^JS 

CD 

Size 
Air  Pipe. 

a   v 
s    i! 

6-^S 
-<j«       Price. 

0)         l-i         : 

S      *      ' 

107 
TOS 

4^ 
4^ 

3 
4 

4 
4 

2.O7 

^68 

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% 
U 

60            

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4>^ 

4 

4.6£ 

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% 

4O           

no 

5% 

3 

5 

2.07 

% 

I 

60           

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5>4 

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5 

2.81 

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112 

cj/ 

3  68 

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5I/ 

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4.6^ 

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114 

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5  06 

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6 

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122 

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5 

RIX  AIR  COMPRESSORS.  127 


PNEUMATIC  GOVERNORS. 

Fig.  54 1/2  shows  the  Pneumatic  Governor  which  the  Fulton 
Engineering  Company  attach  to  all  the  Corliss  Compressors. 
This  Governor  consists  in  a  special  attachment  arranged  in 
connection  with  the  Standard  Corliss  Governor,  which  is 
actuated  by  the  air  pressure.  When  the  pressure  rises  in  the 
air  receiver  the  Governor  balls  are  automatically  lifted  and 
the  hooks  are  thus  tripped  independently  of  the  number  of 
revolutions  which  the  engine  is  making.  When  the  pressure 
falls  in  the  tank  the  device  drops  out  of  the  way  and  the 
engine  is  controlled  by  the  Corliss  Governor  pure  and  simple. 

For  all  ordinary  compressors,  when  desired,  a  Governor  is 
furnished  which  controls  the  admission  of  steam  readily  as  the 
load  varies.  It  is  simple  and  effective  in  its  operation. 


128 


RIX   AIR   COMPRESSORS. 


3s 


31 


cj  *-> 
u  O 
ft> 

S 


THE  RIX  COMPOUND  COMPRESSOR. 



In  speaking  of  the  various  means  in  practise  for  cooling 
the  air  during  its  compression,  reference  has  been  made  here- 
tofore in  this  treatise  to  compounding  the  compressing  cylin- 
ders. The  advantages  of  this  process  are  so  important  that  it 
has  come  into  general  use  and  Compound  Compressors  nowa- 
days are  beginning  to  be  the  rule  rather  than  the  exception. 
It  is  therefore  interesting  to  give  some  explanation  of  this 
method  of  compression. 

The  principle  of  Compound  Compression  can  be  described 
as  follows:  Suppose  that  a  certain  volume  of  air  at  atmospheric 
pressure  and  temperature  is  to  be  raised  to  a  certain  pressure 
and  delivered  into  a  receiver;  in  ordinary,  or  single  stage 
compression,  this  air  is  introduced  into  a  cylinder  wherein  a 
piston  effects  the  compression  and  delivery  of  that  air  at  each 
stroke.  This  compression,  as  we  know,  and  especially  in  fast 
moving  machines,  is  accompanied  by  a  considerable  develop- 
ment of  heat,  which  causes  a  loss  of  efficiency. 

In  the  compound  machine,  air  is  admitted  into  a  cylinder,  as 
before,  but  it  is  compressed  and  delivered  into  a  receiver  at  a 
pressure  smaller  than  the  desired  final  pressure.  In  this  first 
period  or  stage  of  compression  there  is  a  certain  amount  of 
heat  developed,  less,  however,  than  in  the  single  stage  ma- 
chine. The  compressed  air,  after  it  is  delivered  into  this  first 
receiver  at  the  intermediate  pressure,  is  coole'd  by  coming  in 
contact  with  a  number  of  copper  tubes  through  which  cold 
water  is  rapidly  circulated.  This  receiver  is  quite  similar  to 
the  surface  condenser  used  in  marine  engines  and  is  termed 
the  Intercooler,  and  the  compressed  air  leaves  it  after  having 
been  deprived  of  its  heat,  and  reduced  to  practically  the  tem- 
perature of  the  water.  It  is  then  admitted  into  another  smaller 
cylinder  wherein  its  pressure  is  raised  by  another  piston — the 
air  being  again  passed  through  another  intercooler — then  ad- 
mitted into  a  third  cylinder,  and  so  on  until  the  final  desired 
pressure  is  reached. 

The  compression  of  air,  instead  of  being  affected  all  at  once, 
is  therefore  performed  in  several  stages,  each  separated  from 
the  following  one  by  a  cooling  to  the  atmospheric  temperature. 
It  may  be  readily  conceived  that  the  partial  amounts  of  heat 
developed  in  this  series  of  cylinders  are  more  effectively  dealt 
.  with  than  when  the  whole  amount  of  heat  is  liberated  in  a 
single  cylinder.  On  this  ground  the  Compound  Compressor 
will  therefore  possess  a  higher  efficiency  than  the  single  stage 
machine. 

Another  advantage  is  that  the  variation  of  load  on  the 
piston  during  the  stroke  is  less  in  the  compound,  and  conse- 
quently the  strains  on  the  crankpins  are  reduced,  and  a  lighter 


1 3o 


THE   RIX   COMIOUND  COMPRESSOR. 


n 


THE   RIX   COMPOUND   COMPRESSOR.  13! 

flywheel  will  regulate  the  motion  of  the  machine  than  is  the 
case  in  a  single-stage  compressor.  For  instance,  if  we  use  a 
1 2-inch  cylinder  to  compress  air  to  loolbs.  gauge,  in  the  single- 
stage  compressor,  the  load  on  the  piston  during  one  stroke 
will  vary  from  o  to  11,300  Ibs.,  whereas  in  the  compound  ma- 
chine this  load  can  be  made  to  vary  from  o  to  5960  in  all. 

The  principle  of  the  Compound  Compressor  applies  to  any 
number  of  successive  stages,  and,  theoretically,  the  more 
stages  there  are  used  the  nearer  will  the  compression  approach 
the  isothermal.  But,  at  a  practical  standpoint,  the  increased 
number  of  cylinders  is,  of  course,  objectionable,  inasmuch  as 
it  makes  a  heavier  and  more  intricate  machine,  which  will  cost 
more  and  necessitate  more  expenditure  for  maintenance.  The 
frictional  resistances  also  become  greater  with  the  number  of 
cylinders,  and  it  is,  therefore,  readily  seen  that  there  are  some 
practical  limitations  in  the  use  of  this  system. 

It  may  be  stated  that  for  pressures  not  exceeding  200  and 
even  300  Ibs.  per  square  inch,  there  should  not  be  more  than 
two  stages  in  the  compression.  Four  stages  is  the  limit  which 
has  not  been  thus  far  exceeded,  even  with  air  pressure  reach- 
ing to  2000  Ibs.  per  square  inch,  and  even  for  these  high  pres- 
sures three-stage  compressors  are  deemed  amply  sufficient. 

On  the  other  hand,  the  compound  system  would  be  an 
unnecessary  improvement  with  low  pressures.  For  50  or  60 
Ibs.  receiver  pressure  it  is  quite  likely  that  the  percentage  of 
extra  resistances  would  balance  if  not  overcome  the  percentage 
of  gain  in  cooling. 

In  general,  the  advantages  of  a  compound  system  consist  in 
that  less  heat  is  developed  at  each  stroke  of  the  piston,  while 
the  air  under  compression  is  exposed  to  a  larger  cooling  sur- 
face than  in  a  single-stage  machine. 

The  diagram,  Fig.  56,  represents  the  theoretical  adiabatic 
cards  of  a  12x16  single  stage  compressor  and  of  a  tandem  com- 
pound 12  and  7|^xi6,  both  compressing  to  70  Ibs.  gauge.  It 
also  shows  the  expansion  curve  in  a  12x16  steam  cylinder  de- 
veloping with  steam  at  So  Ibs.  gauge  the  same  work  as  the 
single  stage  compressor. 

These  cards  do  not  show  the  variations  of  pressure  of  steam 
and  air,  but  the  variations  of  effective  load  on  the  piston  rod 
of  the  three  cylinders,  and  they  will  serve  for  a  comparison  of 
two  direct-acting  steam  compressors — one  in  the  single  stage 
and  one  in  the  compound  system. 

We  know  already  that  the  aggregate  piston  load  in  the  com- 
pound is  less  than  in  the  single  machine  and  as  the  initial 
loads  are  o  in  both  cases,  the  range  of  variation  is  less  in  the 
compound.  This  allows  a  reduction  in  the  size  of  the  piston 
rods.  It  will  be  noticed  that  the  compound  curve  has  a  sharper 
rise,  since  the  maximum  load  H.  G.  is  reached  at  the  point  / 
of  the  stroke,  while  in  the  single  cylinder  this  same  load  is 
only  reached  at  the  pointy.  The  result  of  it  is  that  during 
this  portion  of  the  stroke,  which  precedes  the  point  of  equal 
loads  in  the  two  compressors,  i.  e.,  the  point  of  intersection  of 


132 


THE   RIX   COMPOUND   COMPRESSOR. 


THE   RIX   COMPOUND   COMPRESSOR. 


133 


the  steam  and  air  curves,  the  difference  of  the  load  between  the 
steam  and  air  pistons  is  smaller  in  the  compound,  where  it  is 
5  V  for  instance,  than  in  the  single  cylinder  compressor, 
where  at  the  same  point  7]  of  the  stroke,  the  difference  is 
5  V. 

The  same  may  be  said  for  the  second  portion  of  the  stroke, 
except  in  the  region //',  but  here  the  discrepancy  is  unim- 
portant, the  piston  loads  being  but  little  at  variance  in  the  two 
compressors,  and  this  region  corresponding  to  the  maximum 
velocities  of  the  pistons. 

As  the  mass  of  moving  pieces,  whose  momentum  is  resorted 
to  for  securing  a  regular  motion,  is  a  function  of  the  actual  dif- 
ference between  the  steam  air  piston  loads,  lighter  regulating 
pieces,  like  flywheels,  will  be  required  in  the  compound  than 
in  the  single  compressor. 

The  same  size  of  steam  cylinder  will  be  found  adopted  in 
practise  with  both  kind  of  compressors,  the  point  of  cut  off 
being,  moreover,  variable. 

A  longer  expansion  of  steam,  combined  with  a  less  weight 
of  machine,  combine  to  win  for  a  compound  compressor  the 
deserved  claim  of  being  a  better  balanced  and  more  economi- 
cal machine  than  the  single  stage. 

It  will  be  seen  that  a  proper  design  of  such  machines  must 
tend  to  an  equal  division  of  the  total  work  among  the  several 
cylinders;  that  the  loads  are  equal  on  each  one  of  the  pistons 
at  any  point  of  the  stroke,  and  that  the  temperature  of  the 
entrance  and  exit  of  the  air  are  the  same  in  all  the  cylinders. 

The  following  table  shows  the  percentage  of  gain  obtained  by 
compounding  as  against  the  single-stage  system,  with  various 
modes  of  compression: 


PERCENTAGE  OF  GAIN  OF    2-STAGE   VS.    I-STAGE    SYSTEMS    OF 
COMPRESSION. 


Ratio   of  Receiver  pressure  to  atmos- 

pheric pressure  

e 

6 

7 

8 

0 

Gain  per  cent  in: 

0 

Adiabatic  Compression  (no  cooling).  .  . 

H-5 

12.8 

13.8 

14.8 

15-9 

Jacketed  Cylinders  

8  OS 

IO.2 

II 

TT    8 

12    5 

Jacketed  Cylinders  cooled  by  spray  in- 

jection  in  the   most   efficient  way 

possible              

6  /\ 

7    S 

8  ? 

8  7 

Q.2 

These  figures  show  that  for  the  usual  air  pressures  the 
amount  of  work  saved  by  compounding  varies  from  9  to  12 
per  cent.  This  is  by  no  means  a  quantity  to  be  neglected. 


134  THE   RIX    COMPOUND   COMPRESSOR. 

We  also  note  that  the  advantage  of  compounding  increases 
with  the  pressure  and  is  more  marked  with  a  poor  than  with  an 
improved  system  of  cooling. 


The  Fulton  Engineering  and  Shipbuilding  Works  do  not 
issue  a  list  of  the  various  sizes  of  their  Compound  Compressors, 
for  the  reason  that  the  relation  between  the  two  cylinders  can 
never  be  fixed,  the  sizes  of  the  initial  cylinders  depending  of 
course  upon  the  quantity  of  air  required,  and  the  size  of  the 
compound  cylinders  depending  entirely  upon  the  pressure 
desired.  Special  estimates  and  specifications  are  furnished 
with  each  compound  machine.  The  following  illustrations 
show  some  of  the  compound  machines  built  by  the  Fulton 
Engineering  and  Shipbuilding  Works,  and  give  an  idea  of 
their  general  style. 

The  Compound  Compressor,  Fig.  60,  shown  in  the  preced- 
ing cut,  illustrates  the  general  style  of  the  Compound  Com- 
pressors built  by  the  Fulton  Engineering  and  Shipbuilding 
Works.  This  Compressor  was  built  for  the  North  Star  Mining 
Company,  of  Grass  Valley,  Cal.,  and  consists  of  Duplex  Tan- 
dem Compound  machines.  The  initial  cylinders  are  18  inches 
in  diameter,  and  the  high  pressure  cylinders  are  10  inches  in 
diameter  by  24-inch  stroke.  The  piston  speed  of  the  machine 
is  440  feet,  which,  while  not  quite  as  economical  as  one  much 
lower,  was  dictated  by  the  conditions  under  which  the  water 
wheel  operated. 

The  air  enters  the  initial  cylinder  at  the  temperature  of  the 
power  room,  which  is  approximately  62  degrees,  and  is  therein 
compressed  to  25  Ibs.  to  the  square  inch  gauge  pressure.  It 
leaves  the  cylinder  at  a  temperature  of  200  degrees  Fahr.  and 
passes  through  an  intercooler  of  about  1000  running  feet  of  i- 
inch  copper  tubes  placed  directly  beneath  the  water  wheel,  and 
which  receives  from  the  wheel  a  continual  shower  of  water  at  a 
temperature  of  about  58  degrees.  This  cools  the  air  to  such  an 
extent  that  it  is  delivered  to  the  high  pressure  cylinders  at  a 
temperature  of  about  60  degrees.  In  these  cylinders  the  air  is 
compressed  to  90  Ibs.  and  is  delivered  from  ihe  cylinders  at  a 
temperature  of  204  degrees  into  6-inch  mains,  which  lead  to  the 
mine.  Indicator  cards  taken  from  the  cylinders  show  that  the 
cylinders  are  doing  equal  work,  and  at  no  revolutions  they 
work  smoothly  and  perfectly. 

Notwithstanding  the  fact  that  some  builders  claim  that 
clearance  has  no  detrimental  effect  upon  the  economy  of  their 
air  compressors,  in  the  Rix  compressors  the  clearance  is  prac- 
tically eliminated,  being  not  to  exceed  one-thirty-second  of  an 
inch  at  each  end  of  the  stroke.  The  cards  taken  from  these 
cylinders  are  practically  square-cornered. 

The  water-jacket  system  is  quite  unique,  it  being  a  duplex 
system— that  is,  there'  is  an  independent  circulation  for  each 
end  of  the  cylinder,  the  water  passing  longitudinally  back  and 
forth  on  the  side  of  the  cylinder  and  from  the  center  in  two 


THK   RIX   COMPOUND   COMPRESSOR. 


HI' 


136 


THE  RIX   COMPOUND   COMPRESSOR. 


THE   RIX   COMPOUND   COMPRESSOR. 


137 


'38 


R1X   COMPOUND  COMPRESSOR. 


o 

fc 


THE  RIX   COMPOUND   COMPRESSOR.  139 

independent  streams,  cooling  the  heads  at  the  same  time.  The 
efficacy  of  this  water  jacket  will  be  noted  in  the  temperatures 
above  given. 

In  testing  for  volumetric  efficiency,  the  receivers  were  care- 
fully measured  a  number  of  times  and  found  to  contain  291 
cubic  feet.  These  were  filled  repeatedly,  and  the  number  of 
revolutions  of  the  machine  accurately  counted  each  time.  All 
of  these  experiments  were  conducted  after  the  machine  had 
been  in  operation  for  a  sufficient  length  of  time  to  reach  its 
maximum  temperature. 

The  barometer  at  the  power  house  is  27.35  inches,  corre- 
sponding to  an  elevation  of  about  2400  feet.  This  gives  an 
atmospheric  pressure  of  13.32  Ibs.  per  square  inch.  At  90  Ibs. 
gauge  pressure  the  ratio  of  compression  would  be  7.7,  and  the 
receiver  containing  291  cubic  feet  represents  2240  cubic  feet 
capacity  of  free  air.  The  average  of  a  great  many  experiments 
showed  that  the  compressor  took  iO2j^  revolutions  to  fill  the 
receiver  from  25  Ibs,  which  is  the  pressure  of  the  initial  cylin- 
der, to  90  Ibs.  At  this  pressure  of  25  Ibs.  gauge  there  is  830 
cubic  feet  of  free  air  in  the  receiver.  The  difference  between 
these  two  capacities,  or  1410  cubic  feet,  would  represent  the 
amount  of  air  which  was  forced  into  the  receiver  at  the  revolu- 
tions stated.  Inasmuch  as  the  temperature  of  the  receiver  is 
somewhat  higher  than  the  temperature  of  the  inlet  air,  there 
should  be  a  deduction  made  from  this  sum  corresponding  to 
that  temperature  of  about  two  per  cent,  making  the  corrected 
amount  delivered  to  the  receiver  1382  cubic  feet. 

The  theoretical  capacity  of  the  compressor,  deducting  the 
piston  rods,  and  at  102^  revolutions,  is  1429  cubic  feet  of  free 
air  per  minute.  The  ratio  between  1382  cubic  feet,  actually 
delivered,  and  1429  cubic  feet,  theoretical  capacity,  is  96.6  per 
cent,  which  represents  the  actual  volumetric  efficiency  of  the 
machine  at  the  present  writing.  This  of  course  will  vary  pro- 
portionately with  the  ratios  of  the  absolute  temperatures  of  the 
inlet  air,  depending  upon  the  season  of  the  year. 

One  peculiarity  about  the  Rix  Compressor,  as  may  be  noted 
from  the  cut,  is  the  fact  that  the  compressor  is  so  arranged  that 
any  cylinder  may  be  disconnected  or  any  end  of  any  cylinder 
may  be  disconnected  without  interfering  with  the  operation  of 
the  machine.  This  feature  is  very  valuable  in  case  of  repairs 
or  accident  to  the  machine. 

To  drive  this  compressor  there  has  been  placed  upon  the 
main  shaft  a  Peltou  water  wheel,  eighteen  feet  in  diameter, 
which  is  believed  to  be  the  largest  tangential  water  wheel  ever 
made. 


THE   PNEUMATIC    TORPEDO   PLANT 
AT  THE  PRESIDIO. 

(Originally  published  in  "Journal  of  Electricity,"  S.  F.) 

The  recent  tests  made  by  the  military  authorities  on  the 
dynamite  guns  at  Fort  Point  may  lend  some  interest  to  a  few 
particulars  regarding  the  Air  Compressing  Plant  which  forms 
the  vital  element  of  this  installation. 

The  contract  for  the  construction  of  the  mechanical  part  of 
it,  with  the  exception  of  the  guns  and  their  immediate  fixtures, 
was  awarded  by  the  Pneumatic  Torpedo  and  Construction  Com- 
pany of  New  York  to  the  Fulton  Engineering  and  Shipbuild- 
ing Works  of  this  city,  upon  the  plans  and  special  designs  of 
Mr.  E.  A.  Rix,  who  supervised  the  construction  of  the  plant. 

The  compression  of  air  is  made  in  three  stages,  from  the 
atmosphere  to  the  working  pressure  of  2000  Ibs.  effective  per 
square  inch.  It  is  performed  in  two  sets  of  horizontal  engines, 
to  both  of  which  the  subsequent  description  applies,  they  being 
in  all  respects  entirely  alike.  The  steam  is  supplied  by  four 
boilers  of  the  Horizontal  Tubular  type,  of  750  H.  P.  capacity, 
arranged  to  work  either  with  natural  or  with  forced  draught. 

Two  steam  cylinders  connected  to  the  same  shaft  by  cranks 
at  an  angle  of  145  degrees  from  each  other,  actuate  in  tandem, 
that  is,  through  their  piston  tail  rods,  each  two  air  cylinders, 
there  being  on  one  side  one  low  pressure  and  the  intermediate 
or  second  stage  cylinder,  and  on  the  other  side  one  low  pres- 
sure and  the  high  pressure  or  finishing  cylinder.  , 

This  duplex  set  therefore  comprises  two  steam  cylinders, 
two  intake  cylinders,  wherein  the  atmospheric  air  is  compressed 
to  about  75  Ibs.  effective,  one  intermediate  cylinder,  carrying 
the  air  pressure  from  75  to  about  400  Ibs.  effective,  and  one  high 
pressure  cylinder,  which  takes  the  air  at  400  Ibs.  and  com- 
presses it  to  2000  Ibs.  effective. 

The  intake  or  low  pressure  cylinders  are  double  acting,  that 
is,  they  have  inlet  and  discharge  valves  at  each  end,  while  the 
intermediate  and  high  pressure  cylinders  are  single  acting,  that 
is,  provided  with  valves  at  one  end  only,  their  pistons  being 
plunger  rams  with  spherical  heads,  connected  to  the  tail  rods 
of  the  intake  cylinders. 

The  special  purpose  which  these  compressors  have  to  serve 
made  their  design  and  construction  subservient  to  conditions 
at  entire  variance  with  the  lines  upon  which  an  air  compressing 
plant  is  usually  established.  The  main  object  of  the  designer, 
when  a  large  power  is  to  be  used,  as  in  the  case  of  the  Fort 
Point  installation,  is  commonly  to  secure  the  greatest  possible 
economy  in  the  production  of  the  compressed  air.  In  the  pres- 
ent instance,  compound  condensing  engines  of  the  most 
approved  type,  and  air  cylinders  working  at  a  moderate  linear 


THE  PNEUMATIC  TORPEDO  PI.ANT. 


141 


8 

02 

2 

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<£ 

£ 


142 


THE   PNEUMATIC  TORPEDO   PI,ANT. 


THE  PNEUMATIC  TORPEDO   PLANT. 


143 


O 


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144  THE   PNEUMATIC  TORPEDO   PI.A.NT. 

piston  speed,  would  present  themselves  to  the  mind  as  advis- 
able. Such  engines  would  be  established  in  view  of  a  regular 
working  speed,  or  approximately  so,  and  everything  would  be 
provided  to  give  the  economical  appliances  a  chance  to  work  to 
their  full  advantage. 

At  Fort  Point  the  primary  requirement  was  to  have  a  plant 
as  little  liable  as  possible  to  getting  out  of  order.  Solidity, 
simplicity,  and  endurance  were  therefore  the  main  points  to  be 
considered,  economy  being  a  desirable  but  decidedly  an  acces- 
sory feature. 

Upon  these  general  lines,  supplemented  by  conditions  of 
capacity  within  a  given  time,  of  efficiency  in  the  means  of  cool- 
ing the  air  and  of  practical  effectiveness  of  several  important 
parts,  the  present  plant  was  designed,  built,  and  erected. 

The  steam  engines  are  non-condensing  and  each  cylinder 
acts  independently;  that  is,  no  compounding  has  been  adopted. 
The  valves  are  provided  with  Meyer's  cut-off,  regulated  by 
hand,  the  Governors  merely  acting  on  the  throttle  in  case 
of  racing.  The  cranks  are  set  at  the  angle  heretofore 
indicated,  in  order  that  the  machine  may  be  balanced  as  nearly 
as  possible  and  yet  the  engines  be  able  to  start  in  any  position. 

In  the  air  cylinders  the  greatest  care  has  been  used  to 
secure  a  cooling  efficiencv  as  high  as  possible.  The  heads  and 
the  barrels  of  the  cylinders  are  water-jacketed,  the  water  dis- 
charge pipes  from  the  jackets  being  in  full  view  and  easily 
accessible,  and  the  supply  of  cooling  water  being  regulated 
according  to  its  temperature  at  the  discharge. 

A  very  elaborate  and  effective  system  of  intercoolers  has 
been  established  between  the  intake  and  intermediate  cylinders 
and  also  between  the  intermediate  and  high  pressure  cylinders. 
These  intercoolers  consist  of  nests  of  copper  pipes  extending 
under  the  floor  in  cemented  trenches,  where  a  stream  of  cold 
water  is  constantly  running.  The  proportions  of  these  inter- 
coolers have  purposely  been  made  very  ample,  and  their  effect- 
iveness is  fully  demonstrated  by  the  low  temperature  of  the 
air  before  it  enters  the  intermediate  and  the  high  pressure 
cylinder,  which  are  given  hereafter. 

A  similar  cooler  is  provided  for  the  air  at  working  pressure 
after  it  leaves  the  high  pressure  cylinder  and  before  reaching 
the  24  forged  steel  storage  tubes,  which  through  a  complete 
system  of  pipes  and  manifolds,  and  also  a  compact  arrangement 
of  valves,  can  be  set  in  communication  with  each  particular 
gun,  or  if  so  desired,  with  a  supplementary  storage  supply 
located  in  the  foundation  of  the  guns. 

That  the  demand  upon  the  compressors  may  vary  during 
action,  within  widely  distinct  limits,  was  exemplified  by  the 
fact  that  while  360  feet  per  minute  is  generally  considered  as  a 
limit  of  piston  velocity  in  water  jacketed  cylinders,  this  velocity 


THE  PNEUMATIC  TORPEDO   PI<ANT. 

£ES 

CF  THE 


CALIFOF. 


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146 


THE   PNEUMATIC   TORPEDO    PI, ANT. 


THE   PNEUMATIC   TORPEDO   PLANT.  147 

has  been,  during  part  of  the  trials,  carried  to  568  feet,  or  an 
excess  of  58  per  cent.  At  this  high  rate  of  speed  no  undue 
heating  could  be  observed  in  the  moving  parts  and  the  absence 
of  jarring  and  of  trepidations  was  the  best  evidence  of  the 
remarkable  strength  and  steadiness  of  the  plant. 

Of  course,  when  working  at  high  speed,  no  claim  is  nor 
could  be  entertained  to  maintaining  a  satisfactory  cooling 
efficiency  in  each  individual  cylinder.  As  before  stated,  the 
iutercoolers  are  of  sufficient  size  to  deal  with  the  heat  liberated 
during  the  compression  even  at  high  speed.  But  when  the 
period  of  compression,  and,  of  course,  the  period  of  effective 
possible  cooling,  lasts  two-fifteenths  of  a  second,  the  heat  units 
passing  through  the  cylinder  walls  during  that  time  cannot  be 
expected  to  be  many.  It  might  be  argued  that  the  Riedler 
compressors  in  Paris  work  at  a  nominal  piston  velocity  of  550 
feet  and  occasionally  733  feet  per  minute,  but  aside  from  the 
fact  that  the  use  of  a  spray  for  cooling  and  of  mechanically 
moved  valves  are  both  combined  to  reduce  the  rise  of  temper- 
ature, the  pressures  in  the  two-stage  Riedler  compressor  are 
considerably  lower,  the  air  being  sent  into  the  mains  at  only 
118  Ibs.  gauge  per  square  inch,  an  insignificant  pressure  as 
compared  to  2000  Ibs. 

Another  point  of  interest  in  the  Fort  Point  plant  is  the 
absence  of  leakage  at  the  stuffing  boxes  of  the  intermediate  and 
high  pressure  rams.  This  point  has  been  the  cause  of  much 
annoyance  in  similar  plants  built  elsewhere,  and  the  present 
arrangement  is  the  outcome  of  long  and  costly  experiments. 

The  friction,  in  a  running  joint  capable  of  holding  2000  Ibs. 
of  air  pressure  against  the  atmospheric,  is  necessarily  enor- 
mous, and  after  the  nature,  the  shape,  and  the  size  of  the 
packing  had  been  determined  upon,  it  became  necessary  to 
keep  the  packing  sufficiently  cool  to  prevent  its  rapid  wear. 
This  is  effected  by  a  special  circulation  of  cold  water  inside  the 
rams,  the  arrangement  being  quite  apparent  on  the  general 
plan,,  and  that  it  is  successfully  effected  can  be  easily  ascer- 
tained. This  water  circulation  also  partly  contributes  to  cool- 
ing the  air  under  compression. 

At  the  normal  rate  of  speed  of  about  400  feet  per  minute  of 
piston  velocity,  the  compressors  supply  to  the  storage  tubes 
460  cubic  feet  of  air  per  hour  at  2000  Ibs.  gauge.  The  annexed 
abstract  from  trials  made  in  view  of  timing  the  production  of 
the  compressors  gives  interesting  evidence  of  the  effectiveness 
of  the  intercoolers  and  of  the  regularity  of  the  temperature  of 
air  at  its  entrance  to  each  cylinder. 

For  a  range  of  final  pressures  comprised  between  800  and 
2000  Ibs.  effective,  the  variation  of  temperature  was  only  8 
degrees  Fahr.  for  the  intermediate  and  3  degrees  Fahr. 
for  the  high  pressure  cylinder,  the  temperature  of  the  engine- 
room  being  71  degrees  Fahr. 


148 


THE  PNEUMATIC  TORPEDO   PI,ANT. 


THE   PNEUMATIC   TORPEDO   PLANT. 


149 


150                           THE   PNEUMATIC  TORPEDO   PI^ANT. 

Gauge  pressure                          Fahr.  temperature  at  entrance  to 

Ibs.  per  sq.  in.     I 

j  1^.  P.  Cylinders. 

I.  P.  Cylinders. 

H.  P.  Cylinders. 

800 

71 

67 

66 

900                             71 

68 

67 

1000                         71 

69 

67 

1100                        71 

69 

67 

1200                                  71 

70 

68 

1300                                  71 

70 

68 

1400 

71 

7i 

68 

1500                                  71 

72 

68 

1600                                  71 

72 

68 

I7OO 

71 

74 

69 

I800 

71 

74 

69 

1900 

71 

73 

69 

2000 

71 

72 

69 

The  discharge  temperature  of  the  low  pressure  cylinders 
gradually  increased  and  then  remained  stationary  at  320  degrees 
Fahr.  The  intermediate  cylinder  discharge  likewise  attained 
a  temperature  of  292  degrees  Fahr.,  and  the  high  pressure 
cylinder,  beginning  at  375  Ibs.  per  square  inch,  and  at  a  tem- 
perature of  66  degrees  Fahr.,  delivered  from  the  intercoolers, 
gradually  rose  in  temperature  as  the  pressure  increased,  until 
it  reached  2000  Ibs.,  and  after  running  at  that  pressure  for- one 
hour,  the  thermometer  indicated  its  maximum,  viz.,  358  degrees 
Fahr. 

The  sum  total  of  those  temperatures,  viz,,  970  degrees,  as 
compared  to  the  adiabatic  temperature  of  single  stage  compres- 
sion to  2000  Ibs.,  which  is  1762  degrees  Fahr.,  indicate  the 
work  saved  by  the  three-stage  method  of  compression  combined 
with  the  jacket  and  ram  cooling  devices. 

The  compression  throughout  the  whole  range  was  practi- 
cally regular,  being  as  an  average  115.1  Ibs.  for  each  500  revolu- 
tions of  both  machines. 

The  mean  of  many  cards  taken  from  the  steam  cylinders 
showed  that  each  compressor  absorbed  342.61  I.  H.  P.,  while 
the  cards  from  the  three  air  cylinders  showed  293  78  I.  H.  P. 
for  each  compressor.  The  work  then  absorbed  by  the  friction, 
inertia,  etc.,  was  48.83  I.  H.  P.  or  14.2  percent  of  the  indicated 
power  employed,  showing  a  mechanical  efficiency  for  the  com- 
pressor of  85.8  per  cent,  which  is  high,  especially  in  view  of 
the  facts  that  the  engines  were  new  and  consequently  stiff  to 
some  extent,  and  also  that  some  extra  friction  is  developed  at 
the  rani  stuffing-boxes  as  compared  with  a  compressor  working 
at  the  usual  air  pressures. 

The  resisting  load  of  48.83  H.  P.  while  the  compressors 
were  doing  full  duty  may  be  compared  with  the  friction  load 
on  the  machine  without  air  pressure,  and  an  interesting  result 


THE   PNEUMATIC   TORPEDO   PI<ANT. 


FORT   POINT 
AIR  COMPRESSING  PLANT 
••»=•  STEAM  *~o  AIR  CARDS  = 


152  THE  PNEUMATIC  TORPEDO  PLANT. 

obtained.  Cards  taken  showed  that  this  friction  load  was  32.4 
H.  P.,  being  .663  of  the  resisting  work  under  load  and  showing 
an  increase  of  50.7  per  cent  in  the  resistances  between  no  load 
and  full  load. 

The  combined  indicator  cards  illustrated  herewith  are 
plotted  from  actual  cards  and  show  a  saving  of  36.8  over  adia- 
batic  single  stage  compression. 

The  boilers  for  this  plant  were  of  the  Return  Tubular  type, 
and  manufactured  by  the  Chandler  &  Taylor  Co.  of  Indian- 
apolis, Ind.;  were  72  inches  in  diameter,  by  16  feet  long,  and 
of  a  nominal  horse  power  of  500,  which  were  increased  by  the 
forced  draught  employed,  to  about  750  horse. 

These  boilers  were  tested  to  150  Ibs.  to  the  square  inch,  and 
fully  satisfied  the  requirements  of  the  Treasury  Department. 
The  forced  draught  was  employed  because  it  was  not  con- 
sidered desirable  to  continue  the  stacks  above  the  roof,  and  thus 
give  an  opportunity  for  invading  forces  to  discover  the  posi- 
tion of  the  plant.  A  short  stack  was  therefore  necessary, 
about  fifteen  feet  in  length,  which  required  the  employment  of 
a  forced  draught.  The  forced  draught  was  instituted  by  two 
Sturtevant  fans,  with  engines  attached,  having  cylinders  three 
inches  in  diameter  by  three  and  a  half  inch  stroke.  These  fans 
delivered  each  12,000  cubic  feet  per  minute  of  free  air,  through 
a  22-inch  main,  which,  passing  underneath  the  battery  of  four 
boilers,  was  connected  to  each  by  a  lo-inch  outlet  underneath 
the  grate  bars.  It  was  found  during  the  test  that  these  fans 
need  be  run  only  to  about  60  per  cent  of  their  capacity. 

The  engines  exhausted  their  steam  into  two  heaters  of 
the  National  type,  of  300  H.  P.  each,  which  furnished  to  the 
boilers  feed  water  at  a  temperature  of  200  degrees  Fahr. 

The  Feed  Pumps  were  of  the  Deanetype,  being  Duplex  and 
two  in  number,  the  steam  cylinders  being  six  inches,  the 
water  cylinders  being  four  inches,  and  the  stroke  being  six 
inches.  At  a  slow  piston  speed  these  pumps  furnished  all  the 
necessary  water,  which  was  drawn  from  the  pits  after  being 
heated  by  the  air  from  the  compressors. 

As  an  auxiliary  there  are  installed  alongside  of  the  Feed 
Pumps  two  Nathan  Injectors  of  300  H.  P.  each,  which  are 
amply  sufficient  to  furnish  all  of  the  water  necessary  to  feed 
the  boilers. 

During  the  test  for  rapidity  of  firing,  while  the  plant  was 
supposed  to  be  strained  to  its  utmost,  the  firemen  had  ample 
time  to  observe  the  operation  of  the  compressor  plant,  showing 
that  the  boilers  were  more  than  sufficient  to  supply  the  steam 
necessary  for  the  proper  operation  of  the  compressors. 

The  electrical  plant  was  furnished  by  the  Electrical  En- 
gineering Company  of  this  city,  and  consisted  of  one  35-kilo- 
Watt  compound  wound  dynamo,  capable  of  being  worked  up 
to  25  per  cent  of  its  rated  capacity  for  thirty  minutes  without 
undue  heat,  and  operated  by  an  Armington  &  Sims  engine. 

This  dynamo  was  connected  by  about  800  feet  of  two-wire, 
insulated  copper  cable,  encased  in  lead  covering,  and  capable 


THR   PNEUMATIC   TORPEDO   PLANT. 


153 


Cu 

5 
<u 

s 


154  THE   PNEUMATIC   TORPEDO   PI^ANT. 

of  carrying  a  current  of  400  amperes,  without  undue  heating. 
This  cable  was  placed  in  and  fastened  to  the  side  of  an 
underground  conduit. 

This  Company  also  placed  in  position,  at  about  ten  feet 
distant  from  the  dynamo,  a  switchboard  of  slate,  and  wired 
complete,  having  three  double-pole  three  hundred  ampere 
knife  switches. 

The  compressed  air,  after  leaving  the  compressors  and 
being  confined  in  the  storage  tanks,  was  distributed  to  the  three 
guns  independently,  through  a  manifold  of  bronze,  having 
attached  five  gauges,  two  registering  2coo  Ibs.,  and  three  1250 
Ibs.,  and  so  arranged  with  valves  that  any  or  all  of  the  guns 
could  be  operated  at  once. 

This  air  is  carried  to  the  underground  storage  reservoirs  of 
the  guns,  through  a  pipe  having  an  outside  diameter  of  2^ 
inches,  and  inside  diameter  of  i^  inches  and  duly  tested  to 
3500  Ibs.  to  the  square  inch  for  tightness. 

From  the  guns  to  these  manifolds  also  there  are  three  cop- 
per pipes,  X  inch  inside  diameter  by  ^  inch  outside  diameter, 
to  register  the  pressures  at  the  manifolds  that  are  contained  in 
the  carriages  of  the  guns. 

This  is  in  general  the  description  of  the  air-compressing 
plant.  We  now  come  to  speak  of  the  guns  themselves,  which 
were  manufactured  at  the  West  Point  foundry  on  the  Hudson, 
each  15  inches  in  diameter,  with  a  length  of  50  feet;  each  gun 
mounted  on  its  carriage,  weighing  about  70  tons,  perfectly  bal- 
ances, and  these  are  mounted  upon  concrete  foundations. 

The  tests  of  these  guns  for  their  mechanical  efficiency, 
which  may  be  called  their  ease  of  operation,  showed  that  they 
could  be  traversed  by  the  electric  motors,  which  were  situated 
in  the  gun  carriage,  in  an  average  of  one  minute,  throughout 
the  entire  360  degrees,  and  they  could  be  elevated  from  extreme 
elevation  to  extreme  depression,  in  from  eight  to  eleven 
seconds.  Any  one  familiar  with  the  length  of  time  necessary 
to  operate  ordinary  powder  guns  by  hand  will  appreciate  the 
fact  that  this  facility  of  operation  is  marvelous. 

For  testing  these  guns  for  mechanical  efficiency,  the 
requirements  were,  first,  that  45  shots  should  be  fired  in  the 
first  hour  and  30  shots  in  the  hour  succeeding.  Inasmuch  as 
the  wastage  of  air  would  be  the  same  whether  actual  projectiles 
were  fired,  or  whether  the  air  was  simply  wasted  through  the 
muzzle  of  the  gun  in  "air  shots,"  no  projectiles  were  fired  in 
this  test,  and  it  was  found  for  the  first  hour  that  45  shots  were 
fired  and  the  compressors  running  at  their  normal  speed  regis- 
tered a  final  pressure  of  1800  Ibs.,  it  being  thus  demonstrated 
that  the  compressors  were  amply  sufficient  to  maintain  any 
requirements  which  might  be  placed  upon  the  gun.  Twenty 
air  shots  were  fired  to  ascertain  the  utmost  rapidity  with  which 


THE   PNEUMATIC  TORPEDO   PLANT. 


155 


35  K.  W,  Dynamo  for  ranging  Dynamite  Guns. 


156  THE   PNEUMATIC  TORPEDO   PI.ANT. 

they  could  be  discharged,  and  the  same  were  discharged  in  7^ 
minutes,  though  the  contract  did  not  require  that  these  shots 
should  be  discharged  inside  of  30  minutes,  it  being  thus 
demonstrated  that  the  compressors  and  the  guns  were  amply 
capable  to  maintain  the  test  required  by  the  Government. 

The  test  for  rapidity  of  firing  with  actual  projectiles  took 
place  next.  The  projectiles  used  were  pieces  of  gas  pipe  12 
inches  in  diameter  and  8  feet  long,  loaded  with  sand.  The 
weight  was  1040  Ibs.  Bach  one  of  the  three  guns  was  required 
to  fire  five  of  these  projectiles  within  twenty  minutes.  The 
test  developed  the  fact  that  these  projectiles  were  all  discharged 
from  each  gun  within  eight  and  one-half  minutes,  and  they 
were  by  far  the  most  interesting  feature  of  the  whole  test. 

Having  no  means  for  maintaining  the  accuracy  of  their 
flight,  these  projectiles  were  nevertheless  thrown  for  the  first 
one-half  distance  of  their  flight  perfectly  accurate;  that  is,  they 
maintained  the  position  of  a  well-directed  projectile,  after 
which  they  tumbled  end  over  end  and  fell  into  the  sea.  With- 
out any  plain  table  measurements  being  taken  upon  them,  they 
apparently  fell  quite  accurately  within  a  small  target. 

The  time  of  flight  of  these  projectiles  averaged  about  nine- 
teen seconds  for  about  2200  yards. 

The  question  of  rapidity  of  firing  and  of  loading  having  been 
determined,  the  next  test  was  one  of  accuracy,  and  the  live 
projectiles  were  discharged  from  these  guns  at  a  distance  of 
5000  yards.  The  projectiles  used  were  of  the  eight-inch  cali- 
ber, the  difference  in  diameter  being  made  up  by  wooden  pis- 
tons in  four  sections  so  that  the  wooden  pieces  would  fly  off 
after  the  projectile  had  left  the  gun,  leaving  it  free  to  make  its 
flight.  The  first  projectile  flew  5000  yards  and  exploded;  the 
second  projectile  flew  5070  yards  and  exploded;  the  third  pro- 
jectile flew  5015  yards  and  exploded;  the  fourth  projectile 
flew  5040  yards  and  exploded;  all  of  these  projectiles  being 
plotted  on  a  plane  table  in  a  rectangle  70  yards  long  by  20 
yards  wide,  the  time  of  flight  being  about  27^  seconds. 

As  a  matter  of  experiment,  two  shots  were  fired  into  the 
hills  of  Marin  County,  at  a  distance  of  3350  yards,  each  with 
the  8-inch  sub-caliber  shell  loaded  with  100  Ibs.  of  dynamite,  the 
first  shot  being  fired  five  days  previous  to  the  second  shot.  The 
shots  struck  within  45  yards  of  each  other  and  exploded  in  a 
perfectly  satisfactory  manner;  in  fact,  the  pits  caused  by  the 
explosion  joined  each  other.  The  larger  shells,  viz.,  the  15- 
inch  full  caliber  projectiles  being  eleven  feet  long  and  weighing 
some  1050  Ibs.,  loaded  with  500  Ibs.  of  nitro-gelatine,  were 
thrown  into  the  sea  at  a  range  of  an  average  of  2100  yards. 
They  exploded  practically  upon  striking  the  water,  throwing 
into  the  air  a  column  of  water  about  100  feet  in  diameter  at  the 


THE  PNEUMATIC  TORPEDO   PI.ANT.  157 

base,  and,  from  the  levels  taken  at  the  gun,  about  400  feet  in 
altitude. 

The  tests  as  above  enumerated  were  perfectly  satisfactory  in 
every  respect  and  exceeded  in  every  way  the  requirements  of 
the  Government.  There  were  no  mistakes  made  and  no  delays 
whatever  caused  by  the  air-compressing  plant  or  the  gun  plant, 
which  probably  exceeded  the  Government  requirements  in  an 
aggregate  of  over  one  thousand  per  cent,  if  the  various  exceed 
percentages  of  the  different  tests  were  added  together,  and 
which  reflected  great  credit  upon  the  manufacturers  of  the 
power  plant,  the  constructing  engineer,  the  manufacturers  of 
the  guns  and  projectiles,  and  also  the  Pneumatic  Torpedo  & 
Construction  Company  of  New  York,  which  contracted  for  and 
thus  successfully  carried  to  completion  their  contract  with  the 
Government. 


€          OP  THE  ^  ^v 

IVERSITT) 
OF  S 


158  ROCK    DRILLS. 


ROCK  DRILLS. 


The  RIX  and  the  GIANT  ROCK  DRILLS  are  manufactured 
in  San  Francisco,  Cal.,  and  their  construction  is  the  result  of  a 
study  of  the  requirements  of  the  Pacific  Coast  in  rock  drilling, 
covering  the  last  twenty  years.  It  has  been  the  aim  of  the  man- 
ufacturers of  these  machines  to  produce  something  which  will  be 
especially  satisfactory  to  the  miners  of  the  Pacific  Coast. 

Many  of  the  improvements  in  these  machines  have  been 
suggested  by  the  operators  of  the  drills  themselves,  to  suit  par- 
ticular conditions,  and  it  has  been  the  aim  of  the  manufacturers 
to  construct  a  machine  which  is  rapid  and  .powerful  in  its 
action. 

The  GIANT  and  the  RIX  DRILLS  are  manufactured  under 
the  following  patents,  controlled  by  EDWARD  A.  RIX. 

U.  S.  PATENTS   AS   FOLLOWS. 

Re-issue  6,7O5  Patent  No.   19O.O99 

Patent  No.   149,013  Patent  No.  2OO,O67 

Patent  No.   152,712  Patent  No.  235,296 

Patent  No.   156,OO3  Patent  No.  235,8  H> 

Patent  No.  109,389  Patent  No.  255,335 

Patent  No.    172,529  Patent  No.  410,334 

Patent  No.   178,214  Patent  No.  454,228 

Patent  No.  490,152 
Others  pending, 


ROCK 


159 


i6o 


ROCK 


ROCK   DRII4<S.  l6l 

Knowing  that  the  average  man  who  runs  a  rock  drill  is  not 
a  skilled  mechanic,  in  the  construction  of  the  RIX  DRILL  the 
aim  has  been  to  produce  a  valve  motion  which  could  not  by  any 
means  whatever  go  wrong  or  fail  to  go  together,  providing  no 
piece  should  be  omitted.  To  accomplish  this  the  entire  VALVE 
MOTION  is  arranged  symmetrical  to  a  line  perpendicular  to  the 
Hue  of  motion  and  passing  through  the  center  of  the  exhaust. 
This  permits  the  main  valve  spool,  the  caps,  plates,  and  buf- 
fers, the  auxiliary  valve,  the  whole  valve  chest,  or  anything  per- 
taining to  it,  to  be  reversed  in  any  way,  and  the  result  is  a 
proper  and  complete  valve  motion,  and  it  also  allows  the  ex- 
haust to  be  turned  in  any  direction  by  simply  using  an  ordinary 
street  elbow. 

All  JOINTS  on  either  of  these  drills  are  scraped,  and  there 
are  no  gaskets  to  get  out  of  order. 

One  of  the  most  annoying  faults  about  imported  rock  drills 
is  the  rubber  buffer,  which  has  to  be  introduced  into  both  heads 
in  order  to  prevent  accident  to  the  heads  by  the  careless  opera- 
tors. Especially  is  this  true  when  steam  is  used,  for  the  rubber 
rapidly  disintegrates  and  interferes  with  the  proper  working  of 
the  machine.  In  both  the  RIX  and  the  GIANT  DRILLS  these 
interior  buffers  are  dispensed  with  and  a  SPIRAL  SPRING  is 
placed  on  the  back  head  of  the  machine  which  does  service  for 
both  heads  and  which  never  wears  out.  In  fact,  a  duplicate 
spring  has  never  been  furnished  for  any  of  these  machines.  A 
flat  bow-spring  does  not  accomplish  the  same  result,  as  it  breaks 
quite  readily,  and  is  generally  replaced  by  a  solid  bar  to  avoid 
further  difficulty. 

Quite  a  feature  with  the  GIANT  and  RIX  DRILLS  is  in  the 
use  of  the  same  sized  COLUMN,  CLAMP,  and  TRIPOD  for  any 
of  the  machines.  The  result  is  that  a  mine  need  purchase  but 
one  sized  mounting,  and  any  drill  will  fit  thereon.  A  3-inch  drill 
may  be  taken  out  of  the  heading  if  hard  rock  is  encountered 
and  a  larger  machine  attached  to  the  same  clamp  at  once, 
without  any  re-setting  of  the  column,  and  this  is  also  found 
especially  valuable  in  upraising  work. 

All  of  the  machines  above  the  2^-inch  size  use  the  same 
hose  and  the  same  COUPLINGS,  and  any  of  the  machines  will 
take  drill  steel  of  any  size  up  to  i%-inch,  and  use  any  shape 
bushing. 

The  above-named  conveniences  are  of  great  consideration, 
and  have  never  failed  to  commend  themselves  to  intelligent 
purchasers.  It  may  be  urged  that  a  COLUMN  which  is  large 
enough  in  diameter  to  properly  carry  a  3-inch  machine  is  too 
small  for  a  3^ -inch  drill.  This  may  be  true  where  the 
machines  stand  away  from  the  column  to  any  extent  and 
where  they  are  being  racked  by  lost  motion  and  where  they 
reciprocate  slowly,  but  with  the  GIANT  and  RIX  machines, 
which  hug  the  column  closely  and  which  have  no  lost  motion  on 
account  of  the  DOUBLE  FEED  NUT  DEVICE,  and  which 


162 


ROCK    DR  11,1,8. 


Fig.  63.— RIX  ROTATING  DEVICE).     Patented. 


ROCK    DRILLS.  163 

reciprocate  fully  fifteen  percent  faster  than  any  other  drill,  it  is 
not  necessary,  and  therefore  a  purchaser  need  not  pay  for  that 
which  he  does  not  require. 


11VJL     11V_V-V_^OCV1.    y  ,       GfcUU     tJ-l*.Ji  V»1V 

which  he  does  not  require. 


The  ROTATING  MOTION  in  these  drills  is  one  of  the  finest 
features  about  them,  and  it  fulfils  perfectly  every  requirement. 
From  the  sketch,  it  will  be  seen  that  it  consists  of  an  internal 
ratchet  engaging  with  swinging  pawls  carried  in  the  head  of 
the  rotating  bar.  A  very  slight  spring  pressure  serves  to 
throw  them  into  contact,  when  by  the  nature  of  the  angles  of 
adjustment  the  pawls  will  be  carried  into  a  pinch  that  cannot 
slip  or  be  broken.  All  the  angles  in  the  ratchet  and  pawls  are* 
right  angles ;  therefore  the  ratchet  may  be  reversed  after  it  is 
worn  on  one  side,  and  equal  service  be  given  to  the  other. 

The  same  is  true  of  the  PAWLS,  and  being  symmetrical,  it 
does  not  matter  which  side  or  end  is  first  presented  for  duty. 

This  feature  of  having  nearly  all  of  the  moving  parts  sym- 
metrical and  reversible  is  quite  a  feature  in  the  construction  of 
these  machines  and  is  of  immense  assistance  in  the  cost  of 
operating  and  convenience,  as  well  as  being  very  useful  in 
emergency. 

It  is  not  necessary  that  these  PAWLS  SHOULD  BE  REVER- 
SIBLE,— a  fact  which  has  been  taken  advantage  of  by  an  East- 
ern drill  manufacturer — and  the  owners  of  the  patent  on  this 
rotating  device  desire  us  to  state  for  them  and  in  their  behalf 
that  the  INTRODUCTION  OF  THIS  SWINGING  PAWL  IN 
A  DRILL  ROTATING  MOTION,  WHKRE  THE  PAWL  IS 
SYMMETRICAL  OR  NON-SYMMETRICAL,  IS  AN  IN- 
FRINGEMENT UPON  THEIR  RIGHTS,  AND  ANY  PAR- 
TIES USING  SAME  WITHOUT  PROPER  LICENSE  FROM 
THESE  ORIGINAL  PATENTEES  WILL  BE  ENJOINED 
FROM  USING  SAME  AND  BE  ALSO  REQUIRED  TO  PAY 
DAMAGES. 

All  rock  drills,  of  either  the  RIX  or  the  GIANT  pattern, 
which  use  compressed  air  as  a  motive  power,  are  supplied  with  a 
FRONT  HEAD,  which  has  no  stuffing  box  but  which  isjnter- 
nally  packed  with  a  leather-cupped  ring,  which  is  absolutely  per- 
fect in  its  action.  This  is  an  old  method  of  packing  a  drill  piston 
rod,  having  been  used  about  twenty  years  ago,  and  is  now  used 
by  other  drill  makers  occasionally.  It  has,  however,  never 
given  any  great  amount  of  satisfaction  and  never  was  absolutely 
tight,  for  the  air  had  always  escaped  through  the  split  in  the 
ring,  and  the  cup  was  not  the  proper  shape. 

The  LEATHER  CUPS,  however,  for  these  drills  are  made 
by  a  machine  especially  constructed  to  shape  the  joints,  form- 
ing a  perfect  interior  and  exterior  cylinder,  one-eighth  of  an 
inch  apart.  There  is  no  split  at  all,  and  they  remain  perfectly 
tight  under  any  pressure  and  last  about  four  months  under 
continuous  wear. 


1 64 


ROCK   DRILLS. 


ROCK   DRILLS. 


'65 


.  65.— GIANT  DRILL  Mounted  on  Tripod. 


166  ROCK    DR1I,I<S. 

The  FEED  NUT  DEVICE  is  another  special  feature  of  both 
of  these  machines.  All  other  rock  drills  are  provided  with  a 
single  feed  nut,  and  this  together  with  the  feed  screw  naturally 
wears  rapidly.  After  wearing  so  that  the  lost  motion  becomes 
apparent,  it  acts  materially  against  the  cutting  power  of  the 
machine,  as  well  as  being  noisy  and  a  fruitful  source  of  acci- 
dents, for  at  every  stroke  of  the  ordinary  rock  drill  it  thumps 
back  and  forth  in  its  cage  to  the  full  extent  of  this  lost  motion. 
The  only  remedy  is  a  new  nut  and  screw. 

In  the  RIX  and  GIANT  DRILLS,  by  means  of  the  double 
feed  nut  all  trouble  of  this  kind  is  avoided.  One  of  the  nuts 
is  secured  to  the  cylinder  of  the  drill  in  a  manner  similar  to  all 
drills;  the  other  has  a  toothed  edge  and  may  be  turned  to  the 
extent  of  a  tooth  at  a  time  as  the  feed  screw  wears.  This 
allows  the  front  edge  of  the  feed  screw  thread  to  work  on  the 
back  edge  of  the  first  feed  nut  thread,  and  the  back  edge  of 
the  feed  screw  thread  to  work  on  the  front  edge  of  the  second 
feed  nut  thread,  thus  furnishing  the  feed  screw  with  practically 
one  perfect-fitting  nut  all  the  time,  and  in  this  manner,  a  feed 
screw  may  be  worn  until  its  threads  break  away  without  any 
lost  motion  being  apparent  in  the  drill.  It  needs  no  comment 
to  show  that  the  drill  uses  FEW  FEED  SCREWS,  in  fact,  the 
life  of  the  screw  is  not  less  than  TWO  YEARS  in  any  case, 
barring  accident. 

The  clamp  is  a  powerful  one,  very  light,  a  perfect  DROP 
STEEL  FORGING,  and  has  but  ONE  BOLT,  so  that  it  is  easy 
to  wqrk,  and  being  very  light  can  be  operated  in  half  the  time 
that  it  requires  for  some  others.  This  clamp  has  been  in  con- 
tinuous use  for  twenty  years  and  has  proved  itself  to  be 
thoroughly  reliable. 

The  PISTON  of  both  the  RIX  and  the  GIANT  DRILLS  is  so 
arranged  that  it  will  receive  any  size  bushing  up  to  i%  inches. 
The  drills  are  always  fitted  with  an  octagon  bushing,  unless 
otherwise  ordered,  for  that  Style  receives  the  steel  just  as  it  is 
manufactured  and  thus  saves  the  expense  of  TURNING  THE 
SHANKS  as  well  as  doing  away  with  the  annoying  breakage 
which  happens  when  the  ends  of  the  steel  are  turned.  The  full 
size  octagon  is  none  too  strong  to  withstand  the  powerful  blows 
delivered  by  these  machines  and  a  much  lower  pressure  must 
be  used  if  the  drill  shanks  are  turned. 

The  COLUMN  MOUNTINGS  used  for  these  machines  are 
similar  to  those  used  by  other  makers,  excepting  that  only  one 
size  is  manufactured.  Other  sizes  are  made  and  kept  in  stock  to 
satisfy  the  ideas  of  customers  who  have  been  used  to  other 
drills,  but  the  increased  size  is  not  necessary  to  a  satisfactory 
working  of  the  machines. 

The  TRIPOD  is  one  furnished  with  universal  joints  to  its 


ROCK   DRrTyIvS. 


i67 


FIG.  65.— 2^-inch  RIX  DRII^  Mounted   on  Tripod. 


i68  ROC 

legs  and  has  stood  the  test  of  twenty  years  of  good  service.  A 
clamp  is  always  used  with  this  tripod;  this  enables  the  head  of 
the  tripod  to  be  used  as  a  short  column,  so  that  the  drill  may 
be  given  a  lateral  motion  of  about  four  inches,  a  feature  which 
is  very  useful  in  drilling  holes  in  uneven  rock  full  of  cracks  or 
fissures,  or  which  from  any  cause  deflects  the  drill  steel. 

In  the  RIX  DRILL  the  VALVE  MOTION  is  in  every  way 
superior  to  anything  which  now  operates  a  rock  drill,  and  one 
of  the  most  noticeable  things  about  the  drill  when  it  is  running 
alongside  of  other  makes,  is  the  wonderful  regularity  of  its 
motion  reciprocating  as  evenly  as  a  steam  engine,  and  deliver- 
ing a  blow  with  much  greater  velocity  than  any  other  machine, 
and  also  more  of  them.  Most  of  the  drill  makers  make  a  claim 
for  an  uncushioned  blow,  and  that  the  valve  does  not  change 
until  after  the  blow  is  struck,  but  these  are  not  facts  which  are 
consistent  with  another  claim  which  they  make;  viz.,  that 
their  machines  are  the  only  ones  which  make  a  variable  stroke. 
None  of  the  standard  makers  claim  that  the  reversing  of  the 
valve  is  dependent  upon  the  striking  of  the  rock,  yet  their 
statements  would  lead  one  to  that  conclusion.  Every  one 
knows  that  the  drills  will  run  at  quite  a  speed  without  striking 
even  the  front  head,  and  any  one  who  examines  their  valve 
mechanism  will  perceive  that  it  is  practically  the  same  for  both 
the  front  and  back  stroke,  and  they  certainly  would  not  like 
the  inference  drawn  that  the  piston  must  strike  the  back  head 
in  order  to  reverse  the  valve. 

The  fact  is  that  all  the  standard  drills  strike  a  cushioned 
blow,  and  the  valve  is  always  reversed  before  the  drill  strikes 
the  rock,  and  this  must  necessarily  be  so  rn  order  to  allow  for 
a  variable  stroke,  and  to  provide  for  a  sufficient  number  of 
strokes.  Drills  have  been  used  in  Europe,  and  many  experi- 
mental ones  made  here  have  been  so  constructed  that  the  valve 
changed  after  the  blow  was  struck.  This,  undoubtedly,  gives 
the  heaviest  blow,  but  the  number  of  the  strokes  is  so  limited 
that  can  be  delivered  in  a  minute,  that  the  machine  could  not 
begin  to  do  the  work  an  ordinary  rock  drill  can  do.  The 
more  the  cushion  in  a  drill,  the  faster  it  will  reciprocate,  and 
the  less  effective  will  be  the  blow.  The  less  the  cushion,  the 
heavier  the  blow  and  the  less  the  number  of  strokes.  The 
shorter  the  working  stroke,  the  greater  the  number  of  strokes 
and  the  less  the  blow,  and  the  less  the  working  pressure,  the 
less  the  number  of  strokes  and  the  less  the  force  of  the  blow. 
Therefore,  in  fashioning  a  rock  drill,  the  result  must  be  a 
mean  between  these  four  relations,  which  shall  give  the  best 
results.  In  other  words,  the  length  of  stroke,  the  amount  of 
cushion,  the  number  of  strokes,  and  the  pressure  used,  must  be 
so  adjusted  with  relation  to  each  other  that  the  best  result  will 
be  produced — allowing,  of  course,  that  the  diameter  of  the 
cylinder  has  been  determined.  All  these  problems  have  been 
very  satisfactorily  solved  in  both  the  RIX  and  the  GIANT 
machines. 


ROCK   DRIIyl^S.  169 

The  VALVE  MOTION  of  the  GIANT  DRILL  is  one  which  is 
operated  directly  from  the  piston  by  mechanical  contact,  and 
this  drill  is  manufactured  to  satisfy  the  beliefs  of  some  drill 
users  that  a  machine  of  this  construction  is  better  than  a  ma- 
chine operating  with  the  auxiliary  valve  motion,  such  as  the 
RIX. 

The  sizes  of  the  GIANT  DRILL  are  made  to  alternate  with 
the  sizes  of  the  RIX,  so  that  the  following  Tables  of  sizes  and 
capacities,  which  represent  a  complete  range,  are  offered  to 
the  public: 


170 


ROCK   DRIIJ,S. 


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172  ROCK 

DUPLICATE  PARTS  OF  THE  RIX 
ROCK  DRILLS. 


i — Rotating  Nut. 

2 — Piston,  bare. 

3 — Piston  Ring. 
4-5 — Sleeve. 

6 — Feed  Nut  (adjustable). 

7— Feed  Nut  (plain). 

8— Yoke  for  Feed  Nuts. 

9 — Lower  Head. 

10 — Leather  Crimp  for  Lower  Head, 
ii — Chuck  Bolts  and  Nuts. 
12 — Chuck  Bushing. 
13 — Chuck  Key. 
14 — Steam  Chest,  bare. 
15 — Main  Valve. 
1 6— Steam  Chest  Cap. 
17— Steel  Cushion  Plate. 
1 8 — Rubber  Cushion. 
19 — Auxiliary  Valve. 
20 — Auxiliary  Valve  Spring. 
21 — Auxiliary  Valve  Claw. 
22 — Oil  Screw. 
23 — Yoke  for  Head  Bolts. 
24 — Head  Spring. 
25 — Cover  for  Ratchet  Ring. 
26— Bottom  Plate  for  Ratchet  Ring. 
27 — Rotating  Bar. 
28 — Cylinder,  bare. 
29— Guide  Block. 
30— Shell  Strip. 
31 — Cylinder  Bolts. 
32— Shell  Bolt. 
33 — Feed  Screw. 
34— Yoke  for  Shell  Bolts. 
35 — Feed  Screw  Handle  (brass). 
36— Pawl. 
37 — Ratchet  Ring. 
38— Pawl  Spring. 
39— Shell  without  Strips  or  Yoke. 
40— Clamp  Wrench. 
41— Steam  Chest  Wrench. 
42— Chuck  Wrench. 


ROCK   DRILLS. 


173 


DUPLICATE  PARTS  OF  THK  R1X  ROCK  DRII,!,. 


174 


ROCK 


DUPLICATE  PARTS  OF  THE  GIANT  DRITVL 


ROCK   DRILLS.  175 

DUPLICATE    PARTS  OF   THE   GIANT 
ROCK  DRILLS. 

i— Rotating  Nut. 

2 — Piston,  bare. 

3 — Piston  Ring. 

4 — Valve  Chest. 

5 — Valve  Chest  Cover. 

6— Feed  Nut  (adjustable). 

7 — Feed  Nut  (plain). 

8— Yoke  for  Feed  Nuts. 

9 — Lower  Head. 

10 — Leather  Crimp  for  Lower  Head, 
ii — Chuck  Bolts  and  Nuts. 
12 — Chuck  Bushing. 
13 — Chuck  Key. 
14 — Valve. 
15 — Valve  Rocker. 
16 — Piston  Ring  Spring. 
17 — Rocker  Pin. 
22 — Oil  Screw. 
23_Yoke  for  Head  Bolts. 
24 — Head  Spring. 
25 — Cover  for  Ratchet  Ring. 
26 — Bottom  Plate  for  Ratchet  Ring. 
27 — Rotating  Bar. 
28 — :Cylinder,  bare. 
30— Shell  Strip. 
31 — Cylinder  Bolts. 
32— Shell  Bolt. 
33 — Feed  Screw, 
34— Yoke  for  Shell  Bolts. 
35 — Feed  Screw  Handle  (brass). 
36— Pawl. 
37 — Ratchet  Ring. 
38— Pawl  Ring. 

39 — Shell  without  Strips  or  Yoke. 
40 — Clamp  Wrench. 
41 — Steam  Chest  Wrench. 
42 — Chuck  Wrench. 


Ij6  ROCK    DRILLS. 


RIX   PLUG   AND   FEATHER   DRILL. 

The  Rix  Plug  and  Feather  Drill,  a  cut  of  which  appears  in 
Fig.  66^,  is  the  smallest  drill  manufactured  by  this  Company. 
It  has  a  two-inch  diameter  cylinder,  from  four  to  five  inch 
stroke,  and  makes  from  seven  hundred  to  nine  hundred  strokes 
per  minute.  It  is  designed  for  drilling  small  holes  about  one 
inch  in  diameter  and  for  depths  up  to  twenty-four  inches. 

For  quarry  work  it  is  mounted  on  a  tripod,  as  shown  in  the 
cut,  and  for  mining  purposes  it  has  the  usual  column  mountings. 
The  tripod  is  one  which  gives  a  wide  range  of  movement. 

The  Drill  itself  weighs  about  65  Ibs.  and  is  extremely  con- 
venient to  handle.  It  is  generally  used  with  seven-inch  steel 
and  the  chuck  is  made  tapering  to  take  the  end  of  the  steel  in 
similar  to  the  way  a  twist  drill  fits  in  its  socket.  This  will  be 
found  most  convenient  in  the  handling  of  these  small  drills. 

This  machine  will  be  found  very  handy  for  many  ranges  of 
work,  including  the  driving  of  wooden  pins  in  caison,  scow,  or 
dry  dock  constructions  where  the  pins  have  to  be  driven  from 
underneath  the  work  being  constructed. 

In  the  use  of  air  it  is  very  economical,  taking  about  twenty- 
five  cubic  feet  of  free  air  per  minute. 


JM  1 


ROCK 


FIG.  65H— RIX  PI/UG  AND  FEATHER  DRII,!,. 


A  FEW  GENERAL  HINTS. 

Buy  a  Compressor  larger  than  you  need. 
Buy  one  which  is  economical. 
Run  it  slow. 

Put  in  good  foundations. 
Have  a  spare  boiler  if  you  can  afford  it. 
Have  a  clean,  ship-shape  engine-room. 
Cover  all  of  your  steam-pipes. 
Provide  large  air-pipes. 

A  generous  sized  receiver  will  come  in  handy. 
Make  as  few  short  turns  as  possible  in  the  air-pipe. 
Use  a  good  cylinder  lubricant. 
Circulate  ample  water  in  the  air  cylinder  jackets. 
Have  some  extra  compressor  valves,    and  change   them  fre- 
quently. 

Put  in  one  or  two  shut-off  valves  in  your  air-pipe. 
Keep  the  receiver  properly  drained. 
Buy  a  rock  drill  of  a  size  best  suited  to  the  work,  and  don't  buy 

any  unless  your  mind  is  made  up  to  do  it  properly. 
Have  plenty  of  steel,  so  your  men  are  not  running  for  drill-bits 

all  the  time. 
Get  a  good  blacksmith,  and  have  him  keep  both  ends  of  the 

Iteel  properly  sized. 
Drill   good-sized  holes,  for  the  powder   does  better   work  at 

the  bottom  of  a  hole. 

Have  an  intelligent  workman  to  run  the  drill. 
Have  an  extra  drill  always  ready  in  the  shop,  and  you  will  find 

less  breakages  and  accidents  occur  to  those  in  use. 
Oil  the  machine  well  before  starting. 
See  that  all  the  nuts  are  tight, 
Be  sure  that  no  dirt  is  in  the  hose  before  it  is  attached  to  the 

machine. 
Keep  the  column  well  jacked  up,  and  have  blocks  of  wood  top 

and  bottom. 
Start  the  holes  on   the  shortest  stroke   of  the  machine,  and 

gradually  lengthen  out  the  stroke  as  the  hole  deepens. 
Feed  the  machine  so  that  the  piston  will  clear  the  front  head. 


GENERAL  HINTS.  179 

In  soft  ground,  make  haste  slowly. 

If  the  steel  gets  stuck  in  the  hole,  strike  it  sharply  until  it 
releases. 

Never  strike  the  chuck. 

Do  not  screw  up  too  hard  on  the  chuck-nuts  or  clamp-bolts, 
for  it  is  perfectly  possible  to  break  them. 

Keep  your  bushings  in  good  order. 

A  bit  of  cast-iron  or  iron  borings  thrown  into  a  fissured  hole 
will  help  it  out. 

A  piece  of  broken  drill-bit  will  often  cause  a  hole  to  run  out. 

Drill  wet  holes  whenever  you  can. 

A  leaky  stuffing-box  will  often  prevent  the  piston  pulling  out 
from  a  tight  hole. 

Never  run  the  drill  against  the  head  to  throw  the  steel  out. 

Do  not  expect  the  drill  to  furnish  brains  to  run  itself. 

Do  not  expect  it  to  run  without  repairs. 

Carry  as  high  a  pressure  as  possible  when  your  rock  is  hard, 
and  calculate  always  that  the  repairs  will  vary,  as  the  pres- 
sure and  also  the  work  done. 

Remember  that  a  rock  drill  is  an  engine,  after  all,  and  the 
fewer  times  it  goes  over  the  dump,  or  is  dropped  off  the 
column,  or  is  blasted  upon,  the  longer  it  will  last. 

Generous  and  faithful  oiling  will  help  a  machine  wonderfully. 

Use  a  good  steam-trap  when  using  a  drill  in  a  quarry. 

A  tripod  must  be  securely  set  to  do  good  work. 

The  same  kind  of  drill-points  do  not  work  equally  well  in 
different  kinds  of  rock. 


i8o 


ROCK   DRIIJ,S. 


FIG.  67. — Column  \vith  Arm. 


FIG.  68.— .Plain  Column. 


Column  Mountings  for  Rock  Drills.     Made  in  any  length.    One  price  for 
all  lengths  under  ten  feet. 


181 


AIR  RECEIVERS. 

In  conjunction  with  an  air  compressor  there  is  generally 
attached  a  reservoir  called  an  air  receiver.  The  purpose  of  this 
is  twofold:  to  collect  the  moisture  which  is  condensed  from  the 
air  after  it  is  compressed,  and  also  to  afford  a  sufficient  volume 
to  receive  the  intermittent  discharges  from  the  compressor,  and 
reduce  them  to  a  continuous  flow  in  the  pipes  leading  from  the 
receiver. 

The  ordinary  receiver  is  fitted  with  an  air  gauge,  a  safety 
valve,  and  a  valve  to  draw  off  the  moisture.  These  are  arranged 
as  shown  in  the  cut  herewith  attached. 

Our  reservoirs  are  made  of  homogeneous  steel,  with  bumped 
heads,  of  a  sufficient  thickness  to  be  tight  at  125  Ibs.  cold 
water  pressure,  for  all  ordinary  plants.  We  prefer  bumped 
heads  because  bracers  are  not  then  necessary.  We  put  three 
cast  iron  feet  on  one  end  of  the  receiver  for  it  to  stand  upon, 
and  sufficiently  high  to  permit  drawing  off  the  entrained  water 
water  easily,  above  the  floor  line. 

We  are  frequently  asked  where  is  the  proper  place  for 
the  receiver — at  the  compressor  or  in  the  mine  ?  We  reply, 
both.  There  never  was  too  much  receiver  capacity  on  any 
plant.  We  do  not  believe  it  essential  to  have  a  very  large 
receiver  near  the  compressor,  providing  there  is  an  oppor- 
tunity to  place  one  further  along  the  pipe.  About  fifteen 
times  the  cylinder  capacity  would,  in  all  ordinary  cases,  keep 
the  gauge  steady  at  the  compressor.  It  would  be  a  great 
benefit  to  systems  having  medium  or  small  size  pipes  to 
have  as  large  a  receiver  capacity  at  or  near  the  point  where 
the  air  is  used,  and  especially  is  this  the  case  where  hoisting 
engines  are  drawing  from  the  air  pipes.  It  requires  no  engi- 
neering knowledge  to  see  that  if  air  receivers  could  be  made 
large  enough  to  diffuse  the  intermittent  work  into  an  average 
draw  on  the  pipe  leading  from  the  compressor,  that  the  com 
pressor  need  be  only  large  enough  for  the  average  work,  whereas 
ordinarily  it  must  be  large  enough  for  the  maximum  work,  and 
consequently  uneconomical. 

It  is  not  generally  practicable  to  have  reservoirs  so  large, 
however,  but  a  reasonable  approach  can  be  made  to  this  capa- 
city without  much  expense.  We  have  known  compressors  to 
do  25  per  cent  more  useful  work  by  putting  receivers  near  the 
point  where  the  air  is  to  be  used,  and  where  numerous  bends 
and  elbows  are  required  in  the  main  pipe. 

When  air  is  drawn  too  fast  through  the  main  pipe,  causing 
a  reduction  of  pressure,  the  increase  of  volume  due  to  the  loss 
pressure  causes  quite  a  marked  increase  in  all  the  frictional 
losses  through  the  system.  We  therefore  advise  receivers  at 
both  ends  of  the  line,  the  smaller  ones  near  the  compressor,  and 
this  is  independent  of  the  amount  of  storage  capacity  in 
the  pipe. 


AIR   RECEIVERS.  183 


DIMENSIONS   OF   AIR   RECEIVERS. 


Diameter,  inches 30  30  30  36       36  42 

Height,  feet 6  8  8         10        12  8 

Thickness  of  Shell,  inches  .  X  XX         XXX 

Thickness  of  Heads,  inches. ><e  Jie  H  H        Y*  H 

Weight 700  900  1200  1400  1600  1800 

No.   of   3X-inch    Drills   Re- 
ceiver is  suitable  for          i  i  2           3          4  5 

Diameter,  inches 42  42  42  48       48  48 

Height,  feet 10  12  16  10         12  16 

Thickness  of  Shell,  inches.    XX  X  Ke  J<e  Xe 

Thickness  of  Heads,  inches  ^  ^  ^  /'e  /<e  Kc, 

Weight 19002000  2100  2^00  2900  3400 

No.  of  3X-inch  Drills  Re- 
ceiver is  Suitable    for         8  10  12  12          15  20 


1 84 


AIR   RECEIVKRS. 


FIG.  70. 


AIR  RECEIVERvS. 


185 


IXDOOOOOO  o  ooooooocta 


i86 


DRII,!,   BITS   AND   HOSE  COUPLINGS. 


SPECIAL    BLACKSMITH   TOOLS    FOR 
DRILL  BITS. 

Fig.  72.  Fig.  73.        Fig.  74.        Fig.  75.          Fig.  76. 


Sow. 


Dolly.         Spreader.       Flatter.          Swedge. 


RIX  PATENT  HOSE  COUPLINGS. 


This  coupling 
is  the  only  coup- 
ling which  will 
stay  on  a  hose 
under  all  condi- 
tions of  use.  They 
have  been  used 
successfully  at  600 
Ibs.  per  square 
inch,  and  are  per- 
fectly reliable. 
The  nature  of  the 
coupling  is  such 


77- 

that  it  is  rigidly 
connected  to  the 
hose,  and  nothing 
but  the  tearing  away 
of  the  hose  itself 
will  separate  it  from 
the  coupling. 


SIZES  AS  FOLLOWS: 

For  i-inch  4  or  5  ply  Hose. 
For  ^-inch  4  or  5  ply  Hose. 
For  2-inch  4  or  5  ply  Hose. 


LUBRICATORS  AND  LUBRICANTS.  187 


LUBRICATORS  AND  LUBRICANTS. 

All  of  our  Compressors  for  ordinary  pressures,  that  is,  up  to 
200  Ibs.  per  square  inch,  are  provided  with  the  Ellis  Sight 
Feed  Lubricator  for  the  air  cylinders.  This,  or  some  similar 
device,  is  the  only  method  for  certain  and  economical  lubrica- 
tion. The  ordinary  oil  cup  delivers  its  entire  contents  in  a 
short  time,  and  there  is  no  means  of  knowing  when  it  requires 
filling,  except  by  opening  it.  For  all  of  our  crank  pins  we  use 
the  Economy  Oiler,  which  feeds  only  when  the  compressor  is 
running.  We  have  reports  stating  that  one  filling  of  one  of 
these  4j^-ounce  oilers  on  the  crank  of  a  lo-inch  compressor 
lasted  four  weeks  of  continuous  run. 

The  ordinary  cylinder  lubricating  oils  will  not  suffice  for 
single  stage  dry  compressor  cylinders,  where  the  compression 
is  almost  adiabatic  from  200  degrees  to  400  degrees,  depending 
on  the  pressures.  Poor  oils  are  decomposed  at  these  tempera- 
tures, and  form  combustible  gases  which  may  explode  with 
dangerous  effect.  There  was  an  explosion  of  this  kind  in  the 
Idaho  Mine,  Grass  Valley,  a  number  of  years  ago,  which 
destroyed  several  hundred  feet  of  6-inch  air  pipe  in  the  shaft. 
Oils  of  at  least  600  degrees  fire  test  should  be  used.  Any  oil 
which  burns  on  the  outlet  valves,  leaving  a  hard,  black, 
rubber-like  substance,  is  not  fit  to  be  used. 

Some  engineers  mix  kerosene  or  coal  oil  with  their  cylinder 
lubricant,  to  cut  the  deposit  and  dirt  from  their  valves,  but  it 
is  a  dangerous  practise  and  will  lead  to  accident,  because  the 
fire  test  of  coal  oil  does  not  ordinarily  exceed  175  degrees  Fahr. 

We  carry  in  stock  special  oils  for  Compressors  and  Rock 
Drills,  known  as 

RIX  COMPRESSOR  OIL. 

RIX  ROCK  DRILL  OIL. 


i88 


AIR   CYUNDER  Oil,  CUP. 


ELLIS  AIR  CYLINDER  OIL  CUP. 

The  cylinders  of  Air  Compressors  are  generally  lubricated 
with  a  plain  oil  cup,  and  a  great  deal  of  difficulty  is  encoun- 
tered in  making  this  feed  steady  enough  for  practical  purposes. 
Either  the  cup  will  not  feed  at  all,  or  it  will  feed  its  entire 

contents  in  a  few  minutes.  The 
lubricator  which  we  are  offer- 
ing is  a  special  lubricator,  de- 
signed so  that  the  pressure  of 
air  in  the  cylinder  will  force  the 
oil  through  a  small  opening, 
which  may  be  regulated,  into 
the  cylinder.  The  drops  may 
be  regulated  as  slow  or  as  fast 
as  necessary,  and  are  made  to 
drop  in  plain  view,  so  as  to 
make  it  a  drop  sight  lubricator, 
something  entirely  new  for  air 
compressing  cylinders  and 
which  we  feel  sure  will  be  a 
great  relief  and  satisfaction  to 
those  who  have  plants  equipped 
with  this  class  of  machinery.  It  goes  without  saying  that  a 
lubricator  of  this  kind  will  use  about  one-half  of  the  oil  that  the 
ordinary  lubricators  require. 

Made  in  either  brass  or  nickel-plated  finish,  in  the  follow- 
ing sizes:  j^-piut,  ^-pint,  j^-pint,  i-pint,  i-quart. 


Fig.  79. 


APPENDIX. 


USEFUL  TABLES, 

TO   BE   USED   IN  THE  CALCULATION   OF 
COMPRESSED   AIR   PROBLEMS. 


The  following  tables  and  data  in  general  will  be  found 
useful  in  the  calculation  of  Compressed  Air  Problems.  These 
tables  have  been  taken  from  Kent's  Hand  Book,  from  The 
Pel  ton  Water  Wheel  Company's  catalogue,  and  from  Carnegie 
Phipps  &  Co.'s  catalogue,  and  we  desire  to  express  to  the 
publishers  of  these  volumes  our  thanks. 


TABLES.  191 

rm<  i  Jii  I;HI;\<  •>  AND  AREAS  OF  CIRCLES 

Advancing  by  Eighths. 


Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

1/64 

.04909 

.00019 

2    % 

7  4613 

4.4301 

6   te 

19.242 

29.465 

1/32 

.09818 

.00077 

7/16 

7.6576 

4.0064 

/4 

19.635 

30.680 

3/64 

.14726 

.00173 

7.8540 

4.9087 

•2 

20.028 

31.919 

1/16 

.19635 

.00307 

9/16 

8.0503 

5.1572 

V£ 

20.420 

33.183 

3/32 

.29452 

.00090 

% 

8.2467 

5.4119 

5,g 

20.813 

34.472 

% 

.39270 

.0122? 

11/16 

8.4430 

5.  0727 

94 

21  206 

35  785 

5/32 

.49087 

.01917 

H 

8.6394 

5.9396 

7Z 

21.598 

37.  122 

3/16 

.58905 

.02761 

13/16 

8.8357 

6.2126 

7t 

21.991 

38.485 

7/32 

.08722 

.03758 

9.0321 

6.4918 

L£ 

22.384 

39.871 

15/16 

9.2284 

6.7771 

IA 

22.776 

41.282 

y* 

.78540 

.04909 

9m 

23.169 

42.718 

9/32 

.88357 

.06-313 

3. 

9.4248 

7.0686 

L£ 

23.56« 

44.179 

5/16 

.98175 

.07670 

1/16 

9  6211 

7.3662 

$£ 

23.955 

45.664 

11/32 

.0799 

.09281 

i^ 

9.8175 

7.6699 

94 

24.347 

47.173 

.1781 

.11045 

3/16 

10.014 

7.9798 

so 

24.740 

48.707 

13/32 

.2763 

.12962 

*4 

10.210 

8.2958 

8. 

25.133 

50.265 

7/16 

.3744 

.15033 

5/16 

10.407L 

8.6179 

££ 

25.525 

51.849 

15/3'^ 

.47:26 

.  17257 

96 

10.603 

8.9462 

/4 

25.918 

53.456 

7/16 

10.799 

9.2806 

9s 

26.811 

55.088 

H 

5708 

.19635 

10.996 

9.6211 

B 

26.  704  v 

56.745 

17/32 

.6690 

.22160 

9/16 

11.192 

9:9678 

9m 

27.096 

58.426 

9/16 

.7671 

.24850 

% 

11.388 

10.321 

•2 

27.489 

60.132 

19/32 

-.8653 

.27688 

11/16 

11.585 

10.680 

% 

27.882 

61.862 

*M» 

.9035 

.30680 

;}4 

11.781 

11.045 

9. 

28.274 

63.617 

21/32 

2.0617 

.33824* 

13/16 

11.977 

11.416 

28.667 

65.397 

11/16 

2.1598 

.37122 

% 

12.174 

11.783 

y. 

29.060 

67.201 

23/32 

2.2580 

.40574 

15/16 

12.370 

12.177 

B 

29.452 

69.029 

4. 

12.566 

12.566 

i^ 

20.845 

70.882 

25/3*2 

2.3562 
2.4544 

.44179 
.47937 

1/16 

12.763 
12.959" 

12.962 
13.364 

P 

30.238 
30.631 

72.760 
74.662 

13/16 

2.5525 

.51849 

3/16 

13.155 

13.772 

/a 

31  .023 

76.589 

27/32 

2.6507 

.55914 

M 

13.352 

14.18C 

10. 

31.416 

78.540 

2.7489 

.60132 

5/16 

13.548 

14,607 

31.809 

80.516 

20/32 

2.8471 

.64504 

96 

13.744 

15.033 

^4 

32.201 

82  516 

15/16 

2.9452 

.69029 

7/16 

13.941 

15.466 

% 

32.594 

84.541 

31/32 

3.0434 

.73708 

M 

14.137 

15.904 

^ 

32.987 

86.590 

9/16 

14.334 

16.349 

% 

33.379 

88.064 

I. 

3.1416 

.7854 

H 

14.530 

16.800 

94 

33.772 

90.703 

1/16 

3.3379 

.8866 

11/16 

14.726 

17.257 

K 

34.165 

92.886. 

i-s 

3.5343 

.9940 

94 

14.923 

17.728 

11. 

34.558 

95.033 

3/16 

3.7306 

1.1075 

13/16 

15.119 

18.190 

^£ 

34.950 

97.205 

M 

3.9270 

1.2272 

% 

15.315 

18.665 

/4 

35.343 

99.402 

5/16 

4.1233 

1.3530 

15/16 

15  512 

19.147 

8 

35.736 

101.62 

^ 

4.3197 

1.4849 

5. 

15.708 

19.635 

i^ 

36.128 

103.87 

7/16 

4.5160 

1.6230 

1/16 

15.904 

20.129 

% 

36.521 

106.14 

^ 

4.7124 

1.7671 

^c 

16.101 

20.629 

94 

36.914 

108.48 

9/16 

4.9087 

1.9175 

3/16 

16.297 

21.135 

7£ 

37.306 

110.75 

11/16 

5.1051 
5.3014 

2.0739 
2.2365 

5/16 

10..  493 
16.690 

21  648 
22.166 

12. 

37.699 
38.092 

113.10 
115.47 

•  94 

5.4978 

2.4053 

% 

16.886 

22.691 

/4 

38.485 

117.86 

13/16 

5.6941 

2.5802 

7/16 

17.082 

23.221 

a/c 

38.877 

120.28 

% 

5.8905 

2.7612 

^ 

17.279 

23.758 

L^ 

39.270 

122.72 

15/16 

6.0868 

2.9483 

9/16 

17.475 

24.301 

M 

39.663 

125.19 

% 

17.671 

24.850 

94 

40.055 

127.68 

6.2832 

3.1416 

11/16 

17.868 

25.406 

7X 

40.448 

130.19 

1/16 

6.4795 

3.3410 

94 

18.004 

25.967 

18. 

40.841 

132.73 

1£ 

6.6759 

3.5466 

13-16 

18.261 

26.535 

^ij 

41.233 

135.30 

3/16 

6.8722 

3.7583 

££ 

18.457 

27.109 

J4 

41.626 

137.89 

7.0686 

3.9761 

1&-16 

18.653 

27.688 

•2 

42.019 

140.50 

^5/16 

7.2649 

4.2000 

18.850 

28.274 

H. 

.    42.412 

143.14 

192 


USEFUL  TABI/ES. 


Diam. 

Circum  . 

Area. 

Diam. 

Circum. 

Area, 

Diam. 

Cireum. 

Area. 

13% 

42.804 

145.80 

21^ 

68.722 

375  .83, 

30^ 

94.640 

712.  T6 

43.197 

148  49 

32. 

69.115 

380.13 

95.083 

718.69 

72 

43.590 

151.20 

L& 

69.508 

384  46 

n 

95.426 

724  64 

14. 

43.982 

153.94 

L£ 

69.900 

388.82 

L^S 

95.81.9 

730.62 

44.375 

156  70 

•2 

70.293 

393.20 

•2 

96.211 

736.62 

it 

44.768 

159.48 

L£ 

70.686 

397.61 

94 

96,604 

742.64 

RZ 

45.160 

162.30 

•2 

71.079 

402.04 

% 

96.997 

748  69 

LjC 

45.563 

165.13 

94 

71  471 

406.49 

31. 

97.389 

754.77 

9m 

45.946 

167.99 

% 

71.864 

410.97 

^& 

97.782 

760.87 

ax 

46.338 

170.87 

28 

72.257 

415  48 

^4 

98.175 

766  99 

v& 

46.731 

173.78 

$ 

72.649 

420.00 

% 

98.567 

773.14 

15 

47.124 

176  71 

73042 

424.56 

Ljji 

98.960 

779.31 

47.517 

179.67 

9m 

73.435 

429.13 

§2 

99.353 

785  51 

/4 

47.909 

182.65 

L£ 

73.827 

433.74 

94 

99.746 

791  73 

•2 

48.302 

185.66 

7m 

74.220 

438.36 

% 

100.138 

79798 

7H 

48.695 

188.69 

94 

74  613 

443.01 

32 

100.531 

804  25 

KZ 

49.087 

191.75 

72 

75.006 

447  69 

/^ 

100.924 

$.0.54 

% 

49.480 

194.83 

24 

75  398 

452.39 

M 

101.316 

816.86 

72 

49.873 

197.93 

75.791 

457.11 

9» 

101  709 

823.21 

16. 

50.265 

201.06 

V4 

76.184 

461.86 

L^ 

102  102 

829.58 

50.658 

204.22 

az 

76  576 

466.64 

7» 

103.494 

836.97 

1^ 

51.051 

207.39 

L£ 

76.969 

471.44 

94 

104.887 

842.39 

a/ 

51.444 

210.60 

K 

77.362 

476  26 

% 

103.280 

848.83 

\& 

51.836 

213.82 

94 

77  754 

481.11 

33 

103  673 

855.30 

% 

52.229 

217.08 

y& 

78.147 

485.98 

^ 

104.065 

861.79 

94 

52.622 

220.35 

25 

78.540 

490.87 

J4 

104.458 

868.31 

7X 

53.014 

223.65 

78.933 

495  79 

•2 

104.851 

874.85 

17 

53.407 

226.98 

J4 

79.325 

500.74 

M 

105.243 

881.41 

53.800 

230  33 

96 

79.718 

505  71 

% 

105  636 

888.00 

/4 

54.192 

233.71 

L<£ 

80.111 

510.71 

94 

106,029 

894.62 

az 

54.585 

237.10 

za 

80.503 

515  72 

% 

106.421 

901.26 

iz 

54.978 

240.53 

?4 

80  896 

520.77 

34 

106.814 

907.92 

£2 

55.371 

243,  98 

7J2 

81.289 

545.84 

J^ 

107.207 

9.14.61 

94 

55.763 

247.45 

26. 

81.681 

530.93 

J^ 

107.600 

921.32 

7? 

56.156 

250.95 

82.074 

536.05 

% 

107.992 

938.06 

iS. 

56.549 

254  47 

^4 

82  467 

541.19 

L^ 

108  385 

934.82 

56.941 

258.02 

•2 

82.860 

546  35 

7& 

108.778 

941.61 

/4 

B7.334 

261.59 

Hi 

83.252 

551  55 

94 

109.170 

948.42 

n 

57.737 

265.18 

§2 

88.645 

556.76 

7^6 

109.563 

955.25 

i^ 

56.  IM 

268.80 

94 

84.038 

562  00 

35 

109.956 

962.11 

78 

58.512 

272.45 

$2 

84.430 

567.27 

110.348 

969.00 

94 

58.905 

276.12 

27 

84.823 

572  56 

/*4 

110.741 

975.91 

% 

69.298 

279.81 

85.216 

577.87 

s 

111.134 

982  .  84 

19 

59.690 

283.53 

M 

85.608 

583.21 

^ 

111.527 

989  80 

£ 

•60083 

287.27 

n 

86  001 

588  57 

•2 

111.919 

996  78 

60.476 

291.04 

i2 

86,394 

593.96 

94 

112.312 

1003  8 

•2 

60.868 

294.83 

78 

86  786 

599.37 

% 

112.705 

1010  8 

i£ 

61.261 

298.65 

94 

87.179 

604.81 

36 

113.097 

1017  9 

7n 

51.054 

302.49 

7? 

87.572 

610.27 

^ 

113.490 

1025  0 

8 

62.046 

306.35 

28. 

87.965 

615.75 

113  883 

1032.1 

ZA 

62.439 

310.24 

88.357 

621.26 

9^ 

114.275 

1039  2 

20 

62,832 

314.16 

V4 

88.750 

626,80 

i^ 

114.068 

1046  3 

^ 

63.245 

318.10 

a? 

89.143 

632.36 

•2 

115.061 

1053.5 

% 

63.617 

322.06 

t^ 

89  535 

637.94 

94 

115,454 

1060  7 

•Z 

64.010 

326.05 

9B 

89  928 

643  55 

?« 

115.846 

1068.0 

76 

64.403 

330,06 

94 

90.321 

649  18 

37 

116  439 

1075  2 

&£ 

64.795 

334  10 

% 

90.713 

654.84 

116.632 

1082  5 

8 

65.188 

338  16 

29 

91  106 

660  52 

/4 

117  024 

1089.8 

t2 

65.581 

342  25 

M 

91  499 

66623 

^ 

117  417 

1097  1 

21 

65.973 

346  36 

y 

91  892 

671  96 

L^ 

117  810 

1104  5 

76 

66  366 

350.50 

H 

92.284 

677  71 

8 

118  202 

1111.8 

^4 

66.759 

354.66 

l^ 

92  677 

683.49 

94 

118.596 

1119.2 

8 

67  152 

358.84 

7H 

93.070 

689.30 

7£ 

118.988 

1126.7 

V£ 

67.544 

363  05 

94 

93  462 

695  18 

38 

119.381 

1134.1 

•2 

67.987 

367  28 

Y& 

93.855 

700  98 

119  773 

1141.6 

94 

68.330 

371  54 

30 

94  248 

706  86 

Vi 

120.166 

1149.1 

USEFUL  TABLES. 


193 


Plain. 

Circum. 

Area, 

Diain. 

Circum- 

Area. 

Diam. 

Circum. 

Area. 

88% 

120.559 

1156.6 

46% 

146.477 

1707.4 

54% 

172.395 

2365.0 

X^ 

120.951 

1164.2 

146.869 

1716.5 

56. 

172.788 

2375.8 

•2 

121.344 

1171.7 

7X 

147.262 

1725.7 

% 

173.180 

2386.6 

3£ 

121.737 

1179.3 

47. 

147.655 

1734.9 

173.573 

2397.5 

B 

122.129 

1186.9 

148.048 

1744.2 

% 

173.966 

2408.3 

39. 

122.522 

1194.6 

/4 

148.440 

1753.5 

ix 

174.358 

2419.2 

^6 

122.915 

"1202.3 

ax 

148.833 

1762.7 

•2 

174.751 

2430.1 

£4 

123.308 

1210.0 

^£ 

149.226 

1772.1 

% 

175.144 

2441.1 

% 

123.700 

1217.7 

% 

149.618 

1781.4 

y6 

175.536 

2452.0 

iZ 

124.093 

1225^4 

94 

150.011 

1790.8 

56. 

175.929 

2463.0 

/6 

124.486 

1233.2 

so 

150.404 

1800.1 

% 

176.322 

2474.0 

94 

124.878 

1241.0 

48 

150.796 

1809.6 

/4 

176.715 

2485.0 

% 

125.271 

1248.8 

^ 

151.189 

1819.0 

B 

177.107 

2496.1 

40. 

125.664 

1256.6 

/4 

151.582 

1828.5 

IX 

177.500 

2507.2 

i^ 

126.056 

1264.5 

B 

151.975 

1837.9 

B 

177.893 

2518.3 

^4 

126.449 

1272.4 

J*> 

152.367 

1847.5 

% 

178.285 

2529.4 

5» 

126.842 

1280.3 

K 

152.760 

1857.0 

7X 

178.678 

2540.6 

^ 

127.2:35 

1288.2 

&£ 

153.153 

1866.5 

57. 

179.071 

2551.8 

% 

127.627 

1:296.2 

% 

153.545 

1876.1 

179.463 

2663.0 

94 

128.020 

1304.2 

49 

153.938 

1885.7 

/4 

179.856 

2574.2 

% 

128.413 

1312.2 

i^ 

154.331 

1895.4 

B 

180.249 

2585.4 

41. 

128.805 

1320.3 

/*4 

154.723 

1905  0 

LX 

180.642 

2596.7 

i^ 

129.198 

1328.3 

B 

155.116 

1914.7 

B 

181.034 

2608.0 

W 

129.591 

1336.4 

i<c 

155.509 

1924.4 

94 

181.427 

2619.4 

B 

129.983 

1344.5 

B 

155.902 

1934,2 

7X 

181.820 

2630.7 

i^ 

130.376 

1352.7 

34 

156.294 

1943.9 

58. 

182.212 

2642.1 

% 

130.769 

1360.8 

% 

156  687 

1953.7 

182.605 

2653.5 

94 

131.161 

1369.0 

50. 

157.080 

1963.5 

ix 

182.998 

2664.9 

% 

131.554 

1377.2 

/^ 

157.472 

1973.3 

ax 

183.390 

2676.4 

42. 

131.947 

1385.4 

ix 

157.865 

1983.2 

IX 

183.783 

2687.8 

^ 

132.340 

1393.7 

% 

158.258 

1993.1 

fiX 

184.176 

2699.3 

/4 

132.732 

1402.0 

i^ 

158.650 

2003.0 

94 

184.569 

2710.9 

B 

133.125 

1410.3 

% 

159.043 

2012.9 

7X 

184.961 

2722.4 

L& 

133.518 

1418.6 

94 

159.436 

2022.8 

69. 

185.354 

2734.0 

B 

133.910 

1427.0 

% 

159.829 

2032.8 

185.747 

2745.6 

94 

134.303 

1435.4 

51. 

160.221 

2042.8 

M 

186.139 

2757.2 

% 

134.696 

1443.8 

ix 

160.614 

2052.8 

3X 

186.532 

2768.8 

43. 

135.088 

1452.2 

J4 

161.007 

2062.9 

IX 

186.925 

2780.5 

M 

135.481 

1460x7 

B 

161.399 

2073.0 

8 

187.317 

2792.2 

y 

135.874 

1469.1 

i^ 

161.792 

2083.1 

94 

187.710 

2803.9 

136.267 

1477.6 

B 

162.185 

2093.2 

7X 

188.103 

2815.7 

/^ 

136.659 

1486.2 

^x 

162.577 

2103.3 

60. 

188.496 

2827.4 

% 

137.052 

1494.7 

TA 

162.970 

2113.5 

IX 

188.888 

2839.2 

'$4. 

137.445 

1503.3 

58. 

163.363 

2123.7 

IX 

189.281 

2851.0 

% 

137.837 

1511.9 

ix 

163.756 

2133.9 

B 

189.674 

2862.9 

44. 

138.230 

1520.5 

/4 

164.148 

2144.2 

1^ 

190.066 

2874.8 

i^ 

138.623 

15'>9.2 

% 

164.541 

2154.5 

B 

190.459 

2886.6 

/4 

139.015 

1537.9 

i^ 

164.934 

2164.8 

94 

190.852 

2898.6 

% 

139.408 

1546.6 

% 

165.326 

2175.1 

7X 

191.244 

2910.5 

ix 

139.801 

1555.3 

3^ 

165.719 

2185.4 

61. 

191.637 

2922.5 

B 

140.194 

1564.0 

so 

166.112 

2195.8 

192.  030 

2934.5 

% 

140.586 

1572.8 

53 

166.504 

2206.2 

IX. 

192.423 

2946.5 

7A 

140.979 

1581.6 

% 

166.897 

2216.6 

ax 

192.815 

2958.5 

46 

141.372 

1590.4 

/4 

167.290 

2227.0 

IX 

193.208 

2970.6 

% 

141.764 

1599.3 

% 

167.683 

2237.5 

fiX 

193.601 

2982.7 

/"4 

142.157 

1608.2 

i^ 

168.075 

2248.0 

94 

193.993 

2994.8 

% 

142.550 

•1617.0 

6X 

168.468 

2258.5 

7X 

194.386 

3006.9 

1£ 

142.942 

1626.0 

% 

168.861 

2269.1 

62. 

194.779 

3019.1 

B 

143.335 

1634.9 

vL 

169.253 

2279.6 

IX 

195.171 

3031.3 

94 

143.728 

1643.9 

54-. 

169.646 

2290.2 

IX 

195.564 

3048.5 

/9 

144.121 

1652.9 

i/ 

170.039 

2300.8 

ax 

195.957 

3055.7 

46 

144.513 

1661.9 

IX 

170.431 

2311.5 

rZ 

196.350 

3068.0 

IX 

144.906 

1670.9 

ax 

170.824 

2322.1 

B 

196.742 

3080.3 

^4 

145.299 

1680.0 

L£ 

171.217 

2332.8 

94 

197.135 

3092.6 

B 

145.691 

1689.1 

% 

171.609 

2343.5 

7X 

197.528 

3104.9 

H 

146.084 

1698.2 

% 

172.002 

2354.3 

63 

197.920 

3117.2 

194 


USEFUL  TABI/ES. 


FIFTH  ROOTS  AND  FIFTH  POWERS. 

(Abridged  from  TRAUTWINE.) 


N 

& 

Power. 

°3 

1(8 

Power. 

^ 

15 

Power. 

°* 

& 

Power. 

°t 
£& 

Power, 

.10 

.000010 

3.7 

693.440 

9.8 

90392 

21.8 

4923597 

40 

102400000 

.15 

.000075 

3.8 

792.352 

9.9 

95099 

22.0 

5153632 

41 

115856','01 

,20 

.000320 

3.9 

902.242 

10.0 

100000 

22.2 

5392186 

42 

130691232 

.25 

.000977 

4.0 

1024.00 

10  2 

110408 

22.4 

5639493 

43 

147008443 

.30 

.002430 

4.1 

1158.56 

10.4 

121665 

22.6 

5895793 

44 

164916224 

.35 

.005252 

4.2 

1306.91 

10.6 

133823 

22.8 

6161327 

45 

184528125 

.40 

.010240 

4.3 

1470.08 

10.8 

146933 

23.0 

6436343 

46 

205962976 

.45 

.018453 

4.4 

1649.16 

11.0 

161051 

23.2 

6721093 

47 

229345007 

.50 

.031250 

4.5 

1845.28 

11.2 

176234 

23.4 

7015834 

48 

254803968 

.55 

.050328 

4.6 

2059.63 

11.4 

192541 

23.6 

7320825 

49 

282475249 

.60 

.077760 

4.7 

2293.45 

11.6 

210034 

23.8 

7636332 

50 

312500000 

.65 

.116029 

4.8 

2548.04 

11.8 

228776 

24.0 

7962624 

51 

345025251 

.70 

.168070 

4.9 

2824.75 

12.0 

248832 

24.2 

8299976 

52 

380204032 

.75 

.237305 

5.0 

3125.00 

12.2 

270271 

24.4 

8648666 

53 

418195493 

.80 

.327680 

5.1 

3450.25 

12.4 

293163 

24.6 

9008978 

54 

459165024 

.85 

.443705 

5/2 

3802.04 

12.6 

317580 

24.8 

9381200 

55 

503284375 

.90 

.590490 

5.3 

4181.95 

12.8 

343597 

25.0 

9765625 

56 

550731776 

.95 

.773781 

5.4 

4591.65 

13.0 

371293 

25,2 

10162550 

57 

601692057 

.00 

1.00000 

5.5 

5032.84 

13.2 

400746 

25.4 

10572278 

58 

656356768 

.05 

1.27628 

5.6 

5507.  S2 

13.4 

432040 

25.6 

10995116 

59 

714924299 

.10 

1.61051 

5.7 

6016.92 

13  6 

465259 

25.8 

11431377 

60 

777600000 

.15 

2.01135 

5.8 

6563.57 

13.8 

500490 

26.0 

11881376 

61 

844596301 

.20 

2.48832 

5.9 

7149.24 

14.0 

537824 

26.2 

12345437 

62 

916132832 

.25 

3.05176 

6.0 

7776.00 

14.2 

577353 

26.4 

12823886 

63 

992436543 

.30 

3.71293 

6.1 

8445.96 

14.4 

619174 

26.6 

13317055 

64 

1073741824 

.35 

4.48403 

6.2 

9161.33 

14  6 

663383 

26.8 

13825281 

65 

1160290625 

.40 

5.37824 

6.3 

9924.37 

14.8 

710082 

27.0 

14348907 

66 

1252332576 

.45 

6.40973 

6.4 

10737 

15.0 

759375 

27.2 

14888280 

67 

1350125107 

.50 

7.59375 

6.5 

11603 

15.2 

811368 

27.4 

15443752 

68 

1453933568 

.55 

8.94661 

6.6 

12523 

15.4 

866171 

27?  6 

16015681 

69 

1564031349 

.60 

10.4858 

6.7 

13501 

15.6 

923896 

27.8 

16604430 

70 

1680700000 

65 

12.2298 

6.8 

14539 

15.8 

984658 

28.0 

17210368 

71 

1804229351 

.70 

14.1986 

6.9 

15640 

16.0 

1048576 

28.2 

17833868 

72 

1934917632 

.75 

16.3141 

7.0 

16807 

16.2 

1115771 

28.4 

18475309 

73 

2073071593 

1.80 

18.8957 

7.1 

18042 

16.4 

1186367 

28.6 

19135075 

74 

2219006624 

1.85 

21.6700 

7.2 

19349 

16.6 

1260493 

28.8 

19813557 

75 

2373046875 

1.90 

24.7610 

7.3 

20731 

16.8 

1338278 

29.0 

20511149 

76 

2535525376 

1.95 

28.1951 

7.4 

22190 

17.0 

1419857 

29.2 

21228253 

7? 

2706784157 

2.00 

32.0COO 

7.5 

23730 

17.2 

1505366 

29.4 

21965275 

78 

2887174368 

2.05 

36.2051 

7.6 

25355 

17.4 

1594947 

29.6 

22722628 

79 

3077056399 

2.10 

40  8410 

7.V 

27068 

17.6 

1688742 

29.8 

23500728 

80 

3276800000 

2.15 

45.9401 

7.8 

28872 

17.8 

1786899 

30.0 

24300000 

81 

3486784401 

2  20 

51.5363 

7.9 

30771 

18.0 

1889568 

30.5 

26393634 

82 

3707398432 

2.25 

57.6650 

8.0 

32768 

18.2 

1996903 

31.0 

28629151 

83 

3939040643 

2.30 

64.3634 

8.1 

34868 

18.4 

2109061 

31.5 

31013642 

84 

4182119424 

2.35 

71.6703 

8.2 

37074 

18.6 

2226203 

32.0 

33554432 

85 

4437053125 

2.40 

79.6262 

8.3 

39390 

18.8 

2348493 

32.5 

36259082 

86 

4704270176 

2.45 

88.2735 

8.4 

41821 

19.0 

2476099 

33.0 

39135393 

87 

4984209207 

2.50 

97.6562 

8.5 

44371 

19.2 

2609193 

33.5 

42191410 

88 

5277819168 

2.55 

107.820 

8.6 

47043 

19.4 

2747949 

34.0 

45435424 

89 

5584059449 

2.60 

118.814 

8.7 

49842 

19.6 

2892547 

34.5 

48875980 

90 

5904900000 

2.70 

143.489 

8.8 

52773 

19.8 

3043168 

35.0 

52521875 

91 

6240321451 

2.80 

172.104 

8.9 

55841 

20.0 

3500000 

35.5 

56382167 

92 

6590815232 

2.90 

205.111 

9.0 

59049 

20.2 

3363232 

36.0 

60466176 

93 

6956883693 

3.  00 

243  000 

9.1 

62403 

20.4 

3533059 

36.5 

64783487 

94 

7339040224 

3.10 

286.292 

9.2 

65908 

20.6 

3709677 

37.0 

69343957 

95 

7737809375 

3.20 

335.544 

9.3 

69569 

20.8 

3893289 

37.5 

74157715 

96 

8153726976 

3.30 

391.354 

9.4 

73390 

21.0 

4084101 

38.0 

79235168 

97 

8587340257 

g.40 

454.354 

9.5 

77378 

21.2 

4282322 

38.5 

84587005 

98 

9039207968 

.50 

525..  219 

9.6 

81537 

21.4 

4488166 

39.0 

90224199 

99 

9509900499 

8.60 

604.662 

9.7 

85873 

21.6 

4701850 

39.5 

96158012 

USEFUL,   TABLES. 


195 


SQUARES,  CUBES  AND  RECIPROCALS. 


Hos. 

Squares. 

Cubes. 

Reciprocals. 

Nos.  Squares. 

Cubes. 

Reciprocals. 

1 

] 

1 

t.  ooooooooo 

51 

2601 

132651 

.019607843 

2 

4 

8 

.500000000 

62 

2704 

140608 

.019210769 

3 

9 

27 

.33333333* 

53 

2809 

148  877 

.018867925 

4 

16 

61 

.250000000 

54 

2916 

157464 

.018518519 

5 

25 

125 

.200UOOUUO 

55 

3025 

166375 

.018181818 

6 

36 

216 

.166666667 

56 

3136 

175  6f  6 

.017857143 

7 

49 

343 

.142857143 

67 

3249 

185193 

.017543860 

8 

64 

512 

.125000000 

58 

3364 

195  112 

.017241379 

9 

81 

729 

.111111111 

59 

3481 

205379 

.016949153 

10 

100 

1000 

.100000000 

60 

3600 

216000 

.016666667 

11 

121 

1331 

.090909091 

61 

3721 

226  981 

.016393443 

12 

144 

1728 

.083333333 

62 

3844 

238  328 

.016129032 

13 

169 

2197 

.0*6923077 

63 

3969 

260047 

.Olo873016 

14 

196 

2744 

.071428571 

64 

4096 

262  144 

.015625000 

15 

225 

3375 

.066666667 

65 

422-5 

274625 

.015384615 

16 

256 

4096 

.062500000 

66 

4356 

287496 

.015151515 

17 

289 

4  913 

.0588-23529 

67 

4489 

3i  0  763 

.014925373 

18 

324 

5832 

.O5555.io56 

68 

4624 

314432 

.014705882 

19 

361 

6859 

.052631579 

69 

4761 

328  509 

.0144927,54 

20 

400 

8000 

.050000000 

70 

4900 

343000 

.014285714 

21 

441 

9261 

.047619048 

71 

5041 

357911 

.01408<507 

22 

484 

10648 

.045451545 

72 

5184 

373218 

.013888889 

23 

529 

12167 

.043478*60 

73 

5329 

389017 

.013698630 

24 

576 

13824 

.041666667 

74 

5476 

405224 

.013513514 

25 

625 

15625 

.040000000 

75 

561:5 

421875 

.013333333 

26 

676 

17576 

.038461538 

76 

57  76 

438  976 

.013157895 

27 

729 

19683. 

.037037037 

77 

5929 

456  5  !3 

.012987013 

28 

784 

21  9)2 

.035714286 

78 

6084 

474552 

.012820513 

29 

841 

24389 

.034482759 

79 

6241 

493039 

.012658228 

80 

900 

27000 

.033333333 

80 

6100 

612000 

.012500000 

31 

961 

29791 

.032258065 

81 

6561 

631441 

.012345679 

32 

1024 

32768 

.031250000 

82 

6724 

651  368 

.012195122 

33 

1089 

35937 

.O3')303030 

83 

68*9 

571  787 

.01204H193 

34 

1156 

39304 

.029411765 

84 

7056 

692  704 

.011904762 

85 

1225 

42875 

.028571429 

85 

7225 

614125 

.011764706 

36 

1296 

46656 

.027777778 

86 

7396 

636056 

.011627907 

37 

1369 

50653 

.027027027 

87 

7569 

658503 

.011494253 

88 

1444 

64872 

.026315789 

88 

7744 

681472 

.011363636 

39 

1521 

59319 

.025641026 

89 

7921 

704  969 

.011235955 

40 

1600 

64000 

.025000000 

90 

8100 

729000 

.011111111 

41 

1681 

68921 

.024390244 

91 

8281 

753571 

.010989011 

42 

1764 

74088 

.02381)9524 

92 

8464 

778688 

.010869565 

43 

1849 

79507 

.0232-55814 

93 

8649 

804357 

.010752f>88 

44 

1936 

85184 

.0227*7273 

94 

8836 

830584 

.010638298 

45 

2025 

91125 

.022222222 

95 

9025 

857375 

.010526316 

46 

2116 

97336 

.0?1789130 

96 

9216 

884736 

.010416667 

47 

2209 

i03  823 

.021J76600 

97 

94(« 

912673 

.010309278 

48 

2304 

11D  592 

.020«3333* 

98 

9604 

941192 

.0101:04082 

49 

2401 

117  649 

.020408153 

99 

9801 

970299 

.010101010 

50 

2500 

125000 

.020000000 

100 

10000 

1000000 

,010000000 

196 


TABI^S. 


SQUARES,  CUBES  AND  RECIPROCALS— CONTINUED. 


Hos. 

Squares. 

Cubes. 

Reciprocals. 

Nos, 

Squares. 

Cubes. 

Reciprocals. 

101 

10201 

1  030  301 

.009900990 

151 

22801 

3  442  951 

.006622517 

102 

10404 

1  061  208 

.009803922 

Io2 

23104 

3511808 

.006578947 

103 

10609 

1092727 

,009708738 

153 

23409 

3581577 

.006535948 

104 

10816 

1  124  864 

.009615385 

154 

23716 

3  652  264 

.006493506 

105 

11025 

1  157  62} 

,009523810 

155 

24025 

3723875 

.006151613 

106 

11236 

1  191  016 

.009433962 

156 

24336 

3796416 

.006410256 

107 

11449 

1  225  043 

.009345794 

157 

24649 

3  869  893 

.006369427 

108 

1  1664 

1  25^  712 

.  0092592  >9 

158 

24964 

3944312 

.006329114 

109 

11881 

1  295  029 

.009174312 

159 

25281 

4  019  679 

.006289308 

110 

12100 

1331000 

.009090909 

160 

25600 

4096001) 

.006250000 

111 

1^2321 

1  367  631 

.009009009 

161 

25921 

4173281 

.006211180 

112 

12544 

1404928 

.008928571 

162 

26244 

42515  8 

.006172840 

113 

12769 

1  442  897 

.008849558 

163 

26569 

4330747 

.0116134909 

114 

12996 

1481541 

.008771930 

164 

26896 

4410944 

.00600*561 

115 

13225 

1  520  875 

.008695652 

165 

27225 

4492125 

.006060606 

116 

13456 

1  560  896 

.008620690 

166 

27556 

4574296 

.006024096 

117 

13689 

1  601  613 

.008547009 

167 

27889 

4  657  463 

.005.988024 

118 

13924 

1613032 

.008474576 

168 

28224 

4741632 

.005952381 

119 

141  61 

1  685  159 

.008403361 

169 

28561 

4826809 

.005917160 

120 

14400 

1728000 

.008333333 

170 

2b900 

4913000 

.005882353 

121 

14641 

1  771  561 

.008264463 

171 

29241 

5000211 

.005847953 

122 

14884 

1  815  848 

.008196721 

172 

29584 

5  088  448 

.00-5813953 

123 

15129 

1  860  867 

.008180081 

173 

29929 

5  177  717 

.005780347 

124 

15376 

1  906  624 

.008064516 

174 

30276 

5  268  024 

.005747126 

125 

15825 

1  953  125 

.008000000 

175 

30625 

5359375 

.005714286 

126 

15876 

2  000  376 

.007936508 

176 

3  09  76 

5  451  776 

.005681818 

127 

1  61  29 

2  048  3S3 

,(X)7874016 

177 

31329 

5  545  233 

,0;  >56  19718 

128 

16384 

2  097  152 

.007*12500 

178 

31684 

6  6'*9  752 

.005617978 

T29 

16641 

2  146  6S9 

.007751938 

179 

32041 

5735339 

.0055(56592 

130 

16900 

2  197  000 

.007692308 

180 

32400 

5  832  000 

.005555556 

131 

17161 

2  248  091 

.007633588 

181 

32761 

5929741 

.005524862 

132 

1  7424 

2  299  968 

.007575758 

182 

33124 

6028568 

.005494--05 

133 

17689 

2  352  637 

.007ol8797 

183 

33489 

6  128  487 

.005464481 

334 

17956 

2  406  104 

.007462687 

J84 

3  as  SB 

6  '229  504 

.005434783 

135 

18225 

2460375 

.007407407 

185 

34225 

6331625 

.005405405 

136 

18496 

2  515  456 

.007352941 

186 

34596 

6434856 

.005376344 

137 

18769 

2571353 

.007299270 

187 

3  49  69 

6  539  203 

.005347594 

138 

19044 

2  628  072 

.007246377 

188 

35341 

6644672 

.005319149 

139 

19321 

26S5619 

.007194*45 

189 

3  57  21 

6751239 

.0052911  05 

140 

19600 

2744000 

.007142857 

190 

36100 

6  859  000 

.005263158 

141 

19881 

2  803  221 

.007092199 

191 

36481 

6967871 

.005235602 

142 

20164 

2863288 

.007042254 

19J 

368*4 

7077888 

.005208333 

113 

20449 

2  924  207 

.006993007 

193 

37249 

7189057 

.005181347 

144 

20736 

2985984 

,006914444 

194 

37636 

7  301  384 

.005154639 

145 

21025 

3048625 

.006898552 

195 

38025 

7  414  875 

,005128205 

146 

2  13  16 

«  112  136 

.006849315 

196 

38416 

7529536 

.005102041 

147 

21609 

3  176  523 

.006802721 

197 

388(i9 

7  «45  373 

.1*6076142 

148 

21904 

3  241  792 

.006756757 

198 

39201 

7762392 

.005050505 

149 

'22201 

8  307  949 

.008711409 

199 

39601 

7880599 

.005025126 

150 

22500 

3375000 

I  .006666667 

200 

40000 

6000000 

.005000000 

USKFUI,  TABLES. 


197 


SQUARES,  CUBES  AND  RECIPROCALS— CONTINUED. 


Hos. 

Squares. 

Cubes. 

Reciprocals. 

Nos. 

Squares. 

Cubes. 

Reciprocals. 

201 

4  04  01 

8120601 

.004975124 

251 

63001 

15813251 

.003934061 

2-32 

40804 

8  242  408 

.004950495 

252 

63504 

16  003  008 

.003968254 

203 

4  1209 

8365427 

.004926108 

253 

64009 

16194277 

.003952569 

201 

4  16  16 

8  489  661 

.01)4901961 

254 

64516 

16  387  064 

.003937008 

205 

42025 

8615  125 

.004878049 

255 

65025 

165S1375 

.003921569 

206 

4  24  36 

8  741  816 

.004854369 

256 

65536 

16777216 

.003906250 

207 

4  28  49 

8  8ti9  743 

.00483U918 

257 

66049 

16  974  593 

.003891051 

208 

4  32  64 

8  998  912 

.004807692 

258 

66564 

17173512 

.003875969 

209 

43681 

9  129  329 

.014784689 

259 

67081 

17  373  979 

.003861004 

210 

44100 

9  261  000 

.001761905 

260 

67600 

17  576  000 

.003846154 

211 

44521 

9393931 

.004739336 

261 

68121 

17779581 

.003^1418 

212 

44944 

9  528  128 

.OJ4716981 

262 

68644 

17  984  728 

.003816794 

213 

45369 

9663597 

.004694836 

263 

69169 

18  191  447 

.003802281 

214 

4  57  96 

9  800  344 

.004672897 

264 

69696 

18  399  744 

.003787*79 

215 

46225 

9938375 

.004651163 

265 

70225 

18  609  625 

.003773585 

216 

46656 

10  077  696 

.004629630 

266 

70756 

18  821  096 

.003759398 

217 

47089 

10  218  313 

.004603*95 

267 

71289 

19  034  163 

.003745318 

218 

47524 

10360232 

.0045*7156 

268 

71824 

19  248  832 

.003731343 

219 

47961 

10503459 

.OP456H210 

269 

72361 

19  465  109 

.003717472 

220 

48400 

10648000 

.004515155 

270 

72900 

19683000 

.003703704 

221 

48841 

10793861 

.004524887 

271 

73441 

19902511 

.003690037 

222 

49284 

10  941  048 

.  00450450  > 

272 

73984 

20  123  648 

.003676471 

223 

49729 

110S9567 

.0044X4305 

273 

74529 

20346417 

.003663004 

224- 

50176 

11239424 

.004464286 

274 

75076 

20570824 

.003649635 

225 

50625 

11390625 

•  ooiiiiiii 

275 

75625 

20  796  875 

.003366364 

226 

61076 

11  643  176 

.004424779 

276 

76176 

21  024  576 

.003623188 

227 

51529 

11697083 

.001405286 

277 

76729 

21  2-53  933 

.003610108 

228 

61984 

11852352 

.001385965 

278 

77284 

21484952 

.003597122 

229 

52441 

120)8989 

.004366812 

279 

77841 

21  717  639 

.003584229 

230 

52900 

12167000 

.001347826 

280 

78400 

21  952  000 

003571429 

231 

63361 

12326391 

.004329004 

281 

78961 

22  18S  041 

.U03558719 

232 

5?824 

12  487  16S 

.004310:345 

232 

79524 

22425768 

.003546099 

233 

54289 

12  649  337 

.0)4291845 

283 

80089 

22  665  187 

.003533569 

234 

64756 

12812904 

.004273504 

284 

80656 

22906304 

.003521127 

235 

55225 

12977875 

.004255319 

285 

81225 

23  149  125 

.003508772 

236 

65696 

13  144  256 

.004237283 

286 

81796 

23  393  656 

.003496503 

237 

561  69 

13  312  053 

.004219409 

287 

82369 

&  639  903 

.003484321 

238 

56644 

13  481  272 

.004:01681 

288 

82944 

23  887  872 

.003472222 

239 

57121 

13  651  919 

.004184100 

289 

8  £521 

24  137  569 

.003460208 

240 

57600 

13824000 

.004166667 

290 

84100 

2438900U 

.00344S276 

241 

58081 

13997521 

.004149378 

291 

84681 

24  642  171 

.003436426 

242 

68564 

14172488 

.004132231 

292 

85264 

24  897  088 

.003424658 

243 

59049 

14  348  907 

.004115226 

293 

85849 

25  153  757 

.003412969 

244 

59536 

14  526  784 

.00409^61 

294 

86436 

25412184 

.003401361 

245 

60025 

14706125 

.004081633 

295 

87025 

25672375 

.003389831 

246 

6  05  16 

14886936 

.004065041 

296 

87616 

25934&S6 

.003378378 

247 

61009 

15069223 

.00404S583 

297 

88209 

28  198  073 

.003367003 

218 

61504 

15  252  992 

.004032>58 

298 

88804 

26463592 

.003355705 

249 

62001 

15  438  249 

.004016061 

299 

89401 

26  730  899 

.003344482 

250 

62500 

15  62-5  000 

.004000000 

3JO 

90000 

27000000 

.003333333 

198 


TABLES. 


SQUARES,  CUBES  AND  RECIPROCALS— CONTINUED. 


Kos. 

Squires 

Cubes. 

'Reciprocals. 

Kos. 

Squires. 

Cubes. 

Reciprocals. 

301 
302 
303 
304 
305 

90601 
91204 
91809 
92416 
93025 

27270901 
27543608 
27  818  127 
28094464 
28372625 

.003322259 
.003311258 
.003300330 

.003289474 
.003278689 

£51 
352 
353 
354 
355 

123201 
523904 
124609 
126316 
126025 

43243661 
43  614  208 
43986977 
44361864 
44  738  875 

.002849003 
.002840909 
.002832861 

.002824859 
.002816901 

306 
307 
308 
309 
310 

93*36 
94249 
94864 
95481 
<*6100 

28652616 
28934443 
29218112 
29603629 
29791000 

.003267974 
.008267329 
.003246753 
.003236246 
.003225806 

356 
357 
£58 
359 
360 

126736 
127449 
128164 
128881 
129600 

45118016 

45499293 
45  882  712 
46268279 
46656000 

.002808989 
.002801120 
.002793296 
.002785515 
.002777778 

311 

312 
313 
314 
315 

96721 
97344 
97969 
98596 
99225 

30090231 
30371328 
30664297 
30  959  144 
31255875 

.003215434 
.003205128 
.(X-3194888 
.003184713 
.003174603 

361 
362 
363 
364 
365 

130321 
131044 
131769 
13  24  96 
133225 

47045881 
47  437  928 
47832147 
48228644 
48627125 

.002770083 
.002762431 

.002754821 
.002747253 
.002739726 

816 
317 
318 
319 
320 

99856 
100489 
101124 
101761 
102400 

31654496 
31  855  013 
32157432 
82  461  759 
32768000 

.003164557 
.003154574 
.003144654 
.003134796 
.003125000 

366 
367 
368 
369 
370 

133966 
134689 
135424 
13  61  61 
136900 

49027896 
49  430  863 
49836032 
50243409 
60663000 

.002782240 

.002724796 
.002717891 
.002710027 
.002702703 

821 
322 
323 
324 
825 

103041 
10  36  84 
104329 
10  49  76 
105625 

33076161 
33  386  248 
33  698  267 
34012224 
34328125 

.003115265 
.003105590 
.003095975 
.003086420 
.003076923 

371 
372 
373 
374 
375 

137641 
13  83  84 
139129 
13  98  76 
140625 

61064811 
61  478  848 
61895117 
62  313  624 
52  734  376 

.002695418 
.002688172 

.00268096-5 
.002673797 
.002666667 

326 

327 
328 
329 
330 

106276 
106929 
10  75  84 
108241 
108900 

34645976 
34  965  783 
35287552 
35  611  289 
35937000 

.003067485 
.003058104 
.003048780 
.003039514 
.003030303 

376 
377 
378 
379 
380 

141376 
142129 
142884 
143641 
144400 

63157376 
53  582  633 
64  010  152 
64439939 
64872000 

.002659574 
.002652520 
.002645503 
.002638522 
.002631679 

331 
332 
333 
334 
335 

109561 
110224 
11  08  89 
111556 
112225 

36264691 
36  594  368 
36926037 
37  259  704 
37595375 

.003021148 
.003012048 
.0030U3003 
.002994012 
.002985076 

381 
382 
383 
3.84 
385 

145161 
14  69  24 
146689 
147456 
148226 

65306341 
65  742  968 
66  181  887 
66  623  104 
67066625 

.002624672 
.002617801 
.002610966 
.002o04lG7 
.002697403 

336 
337 
338 
339 
340 

112896 
113569 
114244 
114921 
116600 

37933056 

38  272  753 
38  614  472 
38958219 
39304000 

.002976190 
.002967359 
.002958580 
,0029498f>3 
.002941176 

386 
387 
3S8 

389 
390 

148996 
149769 
150544 
15  13  21 
152100 

67512456 
67930603 
6S  411  072 
68833869 
59319000 

.002590674 
.002583979 
.002-577320 
.002570(J94 
.002564103 

341 
842 
343 
314 
3-15 

116281 
116964 
117649 
11  83"  36 
119025 

39651821 
40  001  688 
40  353  607 
40  707  684 
41063625 

002932551 
00292-1977 
0029  6452 
002906977 
002898551 

391 
392 
393 
394 
395 

152881 
15  3t>  64 
154449 
15  52  36 
156025 

59  776  471 

60236288 
60698457 
61  162984 
61629875 

.002557545 

.0025-51020 
.002544529 
.002538071 
.002531646 

346 
347 

348 
349 
350 

119716 
120409 
121104 
12  18  01 
122500 

41  421  736 
41781923 
42  144  192 
42  508  549 
42875000 

002890173 
002881844 
002S73561 
0028«5330 
002857U3 

396 

397 
398 
309 
4001 

56816 
15  76  09 
158404 
15  92  01 
10  00  00 

62099136 
62  570  773 
63  044  792 
63  521  199 
64000000 

.002,525253 

.00251K892 
.002512,503 
.002506266 

.002500000 

USEFUL  TABLES. 


199 


SQUARES,  CUBES  AND  RECIPROCALS— CONTINUED. 


Nos. 

Squares. 

Cubes. 

Reciprocals. 

Kos. 

Squares. 

Cubes. 

Reciprocals. 

401 

16  03  01 

64  481  201 

.002493766 

451 

203401 

91  733  851 

.002217295 

402 

16  16  04 

64  964  808 

.002487562 

452 

204304 

92  345  408 

.002212389 

403 

J62409 

65450827 

.002481390 

453 

205209 

92  959  677 

.002207506 

404 

16  32  16 

65  939  264 

.002475248 

454 

206116 

93  576  664 

.002202643 

405 

164025 

66430125 

.002469136 

455 

207025 

94196375 

.002197802 

406 

164836 

66  923  416 

.002463054 

456 

207936 

94818816 

.002192982 

407 

16  56  49 

67  419  143 

.002457002 

457 

20  88  49 

95443993 

.002188184 

408 

166464 

67  917  312 

.002450980 

458 

209764 

96  071  912 

.002183406 

409 

16  72  81 

68  417  929 

.002444988 

459 

21  06  81 

96  702  579 

.002178649 

410 

168100 

68921000 

.002439024 

460 

211600 

97336000 

.002173913 

411 

16  89  21 

09426531 

.002433090 

461 

212521 

97972181 

.002169197 

412 

16  97  44 

69  934  528 

.002427184 

462 

213444 

98611128 

.002164502 

413 

17  05  69 

70  444  997 

.002421308 

463 

21  43  69 

99  252  847 

.002159827 

414 

17  13  96 

70957944 

.002415459 

464 

21  52  96 

99897344 

.002155172 

415 

172225 

71473375 

.0024Q9639 

465 

216225 

100544625 

,002150538 

410 

173056 

71  991  296 

.002403846 

466 

217156 

101  194  696 

.002145923 

417 

17  88  89 

72  51!  713 

.002398082 

467 

218089 

101  847  563 

.002141328 

418 

174724 

73034632 

.002392344 

468 

21  90  24 

102503232 

.002136752 

419 

17  5-5  61 

73  560  059 

.002386635 

469 

219961 

103  161  709 

.002132196 

420 

176400 

74088000 

.002380952 

470 

220900 

103823000 

.002127660 

421 

177241 

74618461 

.002375297 

471 

221841 

104487111 

.002123142 

422 

17  80  84 

75  151  448 

.002369668 

472 

222784 

105154048 

.002118644 

423 

178929 

75686967 

.002364066 

473 

223729 

105823817 

.002114165 

424 

17  97  76 

76  225  024 

.002358491 

474 

224676 

106496424 

.002109705 

425 

180625 

76765625 

.002352941 

475 

225625 

107  171  875 

.002105263 

426 

18  14  76 

77308776 

.002347418 

€76 

226576 

107850176 

.002100840 

427 

18  23  29 

77854483 

.002341920 

477 

227529 

108531333 

.002096436 

428 

183184 

78402752 

.002336449 

478 

228484 

109215352 

.002092050 

429 

18  40  41 

78  953  589 

.002331002 

479 

229441 

109902239 

.002087683 

430 

18  49  00 

79507000 

.002326581 

480 

230400 

110602000 

,002083333 

431 

185761 

80082991 

.002320186 

481 

231361 

111284641 

.002079002 

432 

186S2* 

80621568 

.002314815 

482 

232324 

111980168 

.002074689 

43  J 

187489 

81182737 

.002309469 

483 

233289 

112678587 

.002070393 

434 

18  83  55 

81  746  504 

.002304147 

484 

234256 

113379904 

.002066116 

435 

18  92  25 

82312875 

.002298851 

4S5 

233225 

114064125 

.002061856 

436 

190096 

82881856 

.002293578 

486 

236196 

114  791  256 

.002057613 

437 

190969 

83453453 

.002288330 

487 

237169 

115501303 

.002053388 

438 

191844 

84027672 

.002283105 

488 

238144 

116  214  272 

.002049180 

439 

19  27  21 

84  604  519 

.002277904 

489 

23  91  21 

116930169 

.002044990 

4JO 

193600 

85184000 

.002272727 

490 

240100 

117649000 

.002040816 

441 

19  44  81 

85766121 

.002267574 

491 

211081 

118870771 

.002036660 

442 

195361 

86350888 

.002262443 

492 

242061 

119095488 

.0020-92520 

443 

196249 

86  938  307 

.002257336 

493 

243049 

119823157 

.002028398 

441 

19  71  36 

87  528  384 

.002252252 

494 

244036 

120553784 

.002024291 

443 

198025 

88121125 

.002247191 

495 

245025 

121287375 

,002020202 

446 

198916 

88716536 

.002242152 

496 

246016 

122023936 

.002016129 

447 

199809 

89  314  623 

.0:)2237136 

497 

247009 

122763473 

.002012072 

448 

200701 

89  915  392 

.002232143 

498 

24  80  04 

123505992 

.002008032 

449 

20  16  01 

90518849 

.002227m 

499 

249001 

124  251  499 

.002004008 

450 

202300 

91125000 

.002222222 

500 

250000 

125000000 

.002000000 

USEFUI,  TABLES. 

TEMPER  A  TUiSES,  CENTIGRADE  AN» 
FAHRENHEIT. 


c. 

F. 

P» 
\j* 

F. 

pj 

F. 

C. 

F. 

C. 

F. 

C. 

F. 

C. 

F. 

-40 

-40. 

26 

78.8 

92 

197.6 

158 

816.4 

224 

485.2 

290 

554 

950 

742 

-39 

-38.2 

27 

80.6 

98 

199.4 

159 

818.2 

225 

37. 

300 

572 

960 

760 

-38 

-36.4 

28 

82.4 

94 

201.2 

160 

820. 

226 

438.8 

310 

590 

970 

778 

-3? 

—34  6 

29 

84.2 

95 

203. 

161 

821.8 

227 

440.  G 

320 

608 

980 

796 

-36 

-32.8 

30 

86. 

96 

204.8 

162 

323.6 

228 

442.4 

380 

626 

990 

814 

-35 

-31. 

31 

87.8 

97 

206.8 

168 

825.4 

229 

444.2 

340 

644 

1000 

832 

-34 

—29.2 

32 

89.6 

98 

208.4 

164 

327.2 

230 

446. 

350 

662 

1010 

850 

-33 

—27.4 

33 

91.4 

99 

210.2 

165 

329. 

231 

447.8 

360 

680 

1020 

868 

-32 

-25.6 

34 

93.2 

100 

212. 

166 

330.8 

232 

449.6 

370 

698 

1030 

886 

-31 

-28.8 

35 

95. 

101 

213.8 

16? 

332.6 

233 

451.4 

380 

716 

1040 

904 

-30 

-22. 

36 

96.8 

102 

215.6 

168 

334.4 

234 

453.2 

390 

734 

1050 

922 

-29 

-20.2 

37 

98.6 

103 

217.4 

169 

336.2 

235 

455. 

400 

752 

1060 

940 

-28 

-18.4 

38 

100.4 

104 

219.2 

170 

338. 

236 

456.8 

410 

770 

1070 

958 

-27 

-16.6 

39 

102.2 

105 

221. 

171 

339.8 

237 

458.6 

420 

788 

1080 

976 

-26 

-14.8 

40 

104. 

106 

222.8 

172 

341.6 

238 

460.4 

430 

806 

1090 

1994 

-25 

-13. 

41 

105.8 

107 

224.6 

173 

343.4 

239 

462.2 

440 

824 

1100 

3012 

-24 

-11.2 

42 

107.6 

108 

226.4 

174 

345.2 

240 

464. 

450 

842 

1110 

2030 

-28 

-  9.4 

43 

109.4 

109 

228.2 

175 

347. 

241 

485.8 

460 

860 

1120 

2048 

-22 

-7.6 

44 

111.2 

110 

230. 

176 

348.8 

242 

467.6 

470 

878 

1130 

2066 

-21 

—  5.8 

45 

118. 

111 

231.8 

177 

350.8 

248 

469.4 

480 

896 

1140 

<2084 

-20 

-  4. 

46 

114.8 

112 

233.6 

178 

352.4 

244 

471.2 

490 

914 

1150 

2102 

-19 

-  2.2 

47 

116.6 

113 

235.4 

179 

854.2 

245 

478 

500 

932 

1160 

2120 

-18 

-  0.4 

48 

118.4 

114 

237.2 

180 

856. 

246 

474.8 

510 

950 

1170 

2138 

-17 

+  1.4 

49 

120.2 

115 

239. 

181 

357.8 

247 

476.6 

520 

968 

1180 

2156 

-16 

8.2 

50 

122. 

116 

240.8 

182 

359.6 

248 

478.4 

530 

986 

1190 

2174 

-15 

5. 

51 

128.8 

117 

242.6 

188 

861.4 

249 

480.2 

540 

1004 

1200 

2192 

-14 

6.8 

52 

125.6 

118 

244.4 

184 

363.2 

250 

482. 

550 

1022 

1210 

2210 

-18 

8.6 

53 

127.4 

119 

246.  2 

185 

365. 

251 

488.8 

060 

1040 

1220 

2228 

-12 

10.4 

54 

129.2 

120 

248. 

186 

366.8 

252 

485.6 

570 

1058 

1230 

2246 

-11 

12.2 

55 

131. 

121 

249.8 

187 

368.6 

253 

487.4 

580 

1076 

1240 

2264 

-10 

14. 

56 

132.8 

122 

251.3 

188 

870.4 

254 

489.2 

590 

1094 

1250 

2282 

-  9 

15.8 

57 

134.6 

123 

253.4 

189 

372.2 

255 

49f. 

600 

1112 

1260 

2300 

-  8 

17.6 

58 

136.4 

124 

255.2 

190 

374. 

256 

492.8 

610 

1130 

1270 

2318 

-  7 

19.4 

59 

138.2 

126 

257. 

191 

375.8 

257 

494.6 

620 

1148 

1280 

2336 

-  6 

21.2 

60 

140. 

126 

258.8 

192 

377.6 

258 

496.4 

630 

1166 

1290 

2354 

-  5 

23. 

61 

141.8 

127 

260.  0 

193 

379.4 

259 

498.2 

640 

1184 

1300 

2372 

-  4 

24.8 

62 

143.6 

128 

262.4 

194 

381.2 

260 

500. 

650 

1202 

1310 

2390 

-  3 

26.6 

63 

145.4 

129 

264.2 

195 

383. 

261 

501.8 

660 

1220 

1820 

240« 

-  2 

28.4 

64 

147.2 

130 

266. 

196 

384.8 

262 

308.6 

670 

1238 

1330 

2426 

-  1 

30.2 

65 

149. 

131 

267.8 

197 

386.6 

263 

505.4 

680 

1256 

1340 

2444 

0 

32. 

66 

150.8 

132 

269.6 

198 

388.4 

264 

507.2 

690 

1274 

1350 

2462 

f  1 

38.8 

67 

152.6 

133 

271.4 

199 

890.3 

265 

509. 

700 

1292 

1360 

24  8U 

2 

35.6 

68 

154.4 

134 

273.2 

200 

892. 

266 

510.8 

710 

1810 

1370 

2493 

8 

37.4 

69 

156.2 

135 

275. 

201 

393.8 

267 

512.6 

720 

1328 

1380 

2516 

4 

39.2 

70 

158. 

136 

276.8 

202 

395.6 

268 

514.4 

780 

1346 

1890 

2534 

5 

41. 

71 

159.8 

187 

278.6 

203 

397.4 

269 

516.2 

740 

1364 

1400 

255S 

6 

42.8 

72 

161.6 

138 

280.4 

204 

399.2 

270 

518. 

750 

1382 

1410 

2570 

7 

44.6 

73 

163.4 

139 

282.2 

205 

401. 

271 

519.8 

760 

1400 

1420 

258! 

8 

46.4 

74 

165.2 

140 

284. 

206 

402.8 

272 

521.6 

770 

1418 

1430 

260(1 

9 

48.3 

75 

167. 

141 

285.8 

207 

404.6 

273 

523.4 

780 

1486 

1440 

2624 

10 

50. 

76 

168.8 

142 

287.6 

20S 

406.4 

274 

525.2 

790 

1454 

1450 

2642 

11 

5T.8 

77 

170.6 

143 

289.4 

209 

408.2 

2Z5 

527. 

800 

1472 

1460 

2600 

12 

53.6 

78 

172.4 

144 

291.2 

210 

410. 

276 

528.8 

810 

1490 

1470 

2678 

13 

55.4 

79 

174.2 

145 

293. 

'-^11 

411.8 

277 

580.6 

820 

1508 

1480 

269( 

14 

57.2 

80 

176. 

146 

294.8 

212 

413.6 

278 

532.4 

830 

1526 

1490 

2714 

J5 

59. 

81 

177.8 

147 

296.6 

213 

415.4 

279 

534.2 

840 

1544 

1500 

2732 

16 

60.8 

82 

179.6 

148 

298.4 

214 

417.2 

280 

536. 

850 

1562 

1510 

2750 

I7 

62.6 

83 

181.4 

149 

BOO.  2 

215 

419. 

281 

537.8 

860 

1580 

1520 

2768 

18 

,  64.4 

84 

183.2 

150 

302. 

216 

420.8 

282 

539.6 

870 

1598 

1530 

2786 

19 

66.2 

85 

'185.- 

151 

303.8 

217 

422,6 

283 

541.4 

880 

1616 

1540 

2804 

20 

68. 

80 

186.8 

152 

305.6 

218 

4*4.4 

284 

543.2 

890 

1634 

1550 

2822 

HI 

69.8 

87 

188.6 

153 

307.4 

219 

426.2 

285 

545. 

900 

1652 

1600 

2912 

22 

71.6 

88 

190.4 

154 

309.2 

220 

428. 

.286 

546.8 

910 

1670 

1650 

3002 

28 

73.4 

89 

192.2 

155 

811. 

221 

429.8 

287 

548.6 

920 

1688 

1700 

3092 

24 

75.2 

90 

194. 

156 

312.9 

222 

431.6 

288 

550.4 

930 

1706 

1750 

3182 

35 

77. 

91 

195.8 

157 

314.(i 

223 

433.4 

289 

552.2 

940 

1724 

1800 

8<J72 

USEFUL  TABLES. 

TEMPERATURES,  FAHRENHEIT  AND 
CENTIGRADE. 


c. 

F. 

C. 

F 

C. 

F 

C 

F. 

C. 

F. 

C. 

F. 

C. 

-40 

-40. 

26 

-  3.3 

92 

33.3 

158 

70. 

224 

106.7 

290 

143.3 

360 

182.2 

-39 

-39.4 

27 

—  2.8 

93  1  33.9 

159 

70.6 

225 

107.2, 

291 

143.9 

370 

187.8 

-38 

-38.9 

28 

—  2  2 

94 

:I4.4 

100 

71.1 

226 

107.8 

292 

144.4 

380 

193.3 

—37 

-38.3 

29 

—  1.7 

95 

35. 

161 

71.7 

227 

108.3 

293 

145. 

390 

198.9 

-36 

-37.8 

30 

11 

96 

35.6 

162 

72  2 

228 

108.9 

294 

145.6 

400 

204.4 

-35 

-37.2 

31 

-O'.Q 

97 

36.1 

163 

72.8 

229 

109.4 

295 

146.1 

410 

210. 

-34 

—36.7 

32 

0. 

98 

36.7 

164 

73.3 

230 

110. 

290 

140.7 

420 

215.6 

-33 

-36.1 

33 

-f  0.6 

99 

37.2 

165 

73.9 

231 

110.6 

297 

147.2 

430 

221.1 

-32 

—35.6 

34 

1.1 

100 

37.8 

166 

74.4 

232 

111.1 

298 

147.8 

440 

226.7 

-31 

-35, 

35 

1.7 

101 

38.3 

167 

75. 

233 

111.7 

299 

148.3 

450 

2322 

-30 

—34.4 

36 

2.2 

102 

38.9 

168 

75.6 

234 

112.2 

300 

148.9 

4601237.8 

—29 

-33.9 

37 

2.8 

103 

-39.4 

169 

76.1 

235 

112.8 

301 

1494 

470  243.3 

—28 

-33.3 

38 

3.3 

104 

40. 

170 

70.7 

236 

113.3 

30-<2 

150. 

480 

2489 

-27 

-32.8 

39 

3.9 

105 

40.6 

171 

77.2 

237 

113.9 

303 

150.6 

490 

254.4 

-26 

-32.2 

40 

4.4 

106 

41.1 

172 

77  8 

238 

114.4 

301 

151.1 

500 

260. 

—25 

-31.7 

41 

5. 

107 

41.7 

173 

78.3 

239 

115. 

305 

151.7 

510 

265.6 

—24 

-31.1 

42 

5.6 

108 

42.2 

174 

78.9 

240 

115.6 

300 

152.2 

520 

271.1 

-23 

-30.6 

43 

6.1 

109 

42.8 

175 

79.4 

241 

116.1 

307 

152.8 

530 

276.7 

-22 

—30. 

44 

6.7 

110 

43.3 

176 

80. 

242 

116.7 

308 

153.3 

540 

282.2 

-21 

—29.4 

45 

7.2 

111 

43.9 

177 

80.6 

243 

117.S 

309 

153.9 

550 

287.8 

-20 

-28.9 

46 

7.8 

112 

44  4 

178 

81.1 

244 

117.8 

310 

154.4 

560 

293.3 

-19 

—28.3 

47 

8.3 

113 

45. 

179 

81.7 

245 

118.3 

311 

155. 

570 

298.9 

-18 

—27.8 

48 

8.9 

114 

45.6 

t80 

82.2 

246 

118.9 

312 

155.6 

580 

804.4 

-17 

—27.2 

49 

9.4 

115 

46.1 

181 

82.8 

247 

119.4 

313 

156-.1 

590 

310. 

-16 

—26.7 

50 

10. 

116 

46.7 

182 

83.3 

248 

120. 

314 

156.7 

600 

315.6 

-15  i-26.1 

51 

10.6 

117 

47.2 

183 

83.9 

249 

120.6 

315 

157.2 

610 

321.1 

-14  -25.6 

52 

11.1 

118 

47.8 

184 

84.4 

250 

121.1 

816 

157.8 

620 

326.7 

—13  1-25. 

53 

11.7 

119 

48.3 

185 

85. 

251 

121.7 

317 

158.3 

680 

332.2 

-12 

—24.4 

54 

12.2 

120 

48.9 

186 

85  6 

252 

122.2 

318 

158.9 

640 

337.8 

—11 

-23.9 

55 

12.8 

121 

49.4 

187 

86.1 

253 

122.8 

319 

159.4 

650 

343.3 

—10 

-23.3 

56 

13.3 

122 

50. 

188 

86.7 

254 

123.3 

320 

160. 

660 

348.9 

-  9 

oo  g 

57 

13.9 

123 

50.6 

189 

87.2 

255 

123.9 

321 

160.6 

670 

354.4 

-  8 

—S!  2 

58 

14.4 

124 

51.1 

190 

87.8 

256 

124.4 

322 

161.1 

680 

360. 

—  7 

-21.7 

59 

15. 

125 

51.7 

191 

88.3 

257 

125. 

323 

161.7 

690 

365.6 

—  6 

-21.1 

60 

15.6 

126 

52.2 

192 

88.9 

258 

125.6 

324 

162.2 

700 

371.1 

—  5 

-20.6 

61 

16.1 

127 

52.8 

193 

89.4 

259 

126.1 

325 

162.8 

710 

376.7 

-  4 

-20. 

62 

16.7 

128 

53.3 

194 

90. 

t>00 

126.7 

326 

163.3 

7201382.2 

-  3 

—19.4 

63 

17.2 

129 

53.9 

195 

90.6 

261 

127.2 

327 

163.9 

730  387.8 

—  2 

-18.9 

64 

17.8 

130 

54.4 

196 

91.1 

262 

127.8 

328 

164.4 

740 

393.3 

—  1 

—18  3 

65 

18.3 

131 

55 

197 

91.7 

263 

128.3 

829 

165. 

750 

398.9 

0 

-17.8 

66 

18.9 

132 

55.6 

198 

92.2 

264 

128.9 

330 

165.6 

760 

404.4 

+  1 

-17.2 

67 

19.4 

133 

56.1 

199 

92.8 

:>65 

129.4 

331 

166.1 

770 

410. 

2 

-16.7 

68 

20. 

134 

56.7 

200 

93.3 

266 

130. 

332 

166.7 

780 

415.6 

3 

-16.1 

69 

20.6 

135 

57.2 

201 

93.9 

267 

130.6 

333 

167.2 

790 

421.1 

4 

—15.6 

70 

21.1 

136  |  57  8 

202 

94.4 

268 

131.1 

334 

167.8 

800 

426.7 

5  -T5. 

71 

21.7 

137  58.3 

203 

95. 

269 

131.7 

335 

168.3 

810 

432.2 

6  —14.4 

72 

22.2 

138 

58.9 

204 

95.6 

270 

132.2 

336 

168.9 

820 

437.8 

7  -13.9 

73 

22.8 

139 

59.4 

205 

96.1 

271 

132.8 

337 

169,4 

830 

443.3 

8  1—13.3 

74 

23.3 

110 

60. 

206 

96.7 

272 

133.3 

ass 

170. 

840 

448.9 

9 

—12.8 

75 

23.9 

141 

60.6 

207 

97.2 

273 

133.9 

339 

170.6 

850 

454.4 

10 

-12.2 

76 

2*4.4 

142 

61.1 

208 

97.8 

274 

134.4 

340 

171.1 

860 

460. 

11 

-11.7 

77 

25. 

143 

61.7 

209 

98.3 

275 

135. 

341 

171.7 

870 

465.6 

12 

—11.1 

',8 

25.6 

144 

62.2 

210 

98.9 

270 

135.6 

342 

172.2 

880 

471.1 

13 

-10.6 

79 

26.1 

145 

62.8 

211 

99  4 

277 

136.1 

343 

172.8 

890 

476.7 

14 

-10. 

80 

26.7 

146 

63.3 

212 

100. 

278 

136.7 

344 

173.3 

900 

482.2 

15 

—  9.4 

81 

27.2 

147 

63.9 

213 

100.0 

279 

137.2 

345 

173.9 

910 

487.8 

16 

-  8.9 

82 

27.8 

148 

64.4 

214 

101.1 

280 

137.8 

346 

174.4 

920 

493.3 

17 

—  8.3 

83 

28.3 

149 

65. 

215 

101.7 

281 

138.3 

347 

175. 

930 

498.9 

18 

-  7.8 

84 

28.9 

150  (  65.6 

210 

102.2 

282 

138.9 

348 

175.6 

940 

504.4 

19 

—  7.2 

85 

29.4 

151 

66.1 

217 

102.8 

283 

139.4 

349 

176.1 

950 

510. 

20 

—  6.7 

86 

30. 

152 

66.7 

218 

103.3 

284 

140. 

350 

176.7 

960 

515.6 

21 

—  6.1 

87 

30.6 

153 

67.2 

219 

103.9 

285 

140.6 

351 

177.2 

970 

521.1 

22 

-  5.6 

88 

31.1 

154 

67.8 

220 

104.4 

286 

141.1 

352 

177.8 

980 

526.7 

23 

—  5. 

89 

31.7 

155 

68.3 

2',M 

105. 

287 

141.7 

353 

178.3 

990 

532.2 

24 

-  4.4 

90 

32.2 

156 

68.9 

222 

105.6 

288 

142.2 

354 

178.9 

000 

537.8 

iff 

T-  3.9 

91 

32.8 

157  I  69.4 

223 

106.1 

289 

142.8 

355 

179.4 

010 

543.3 

USEFUL,  TABLES. 


DECIMALS  OF    A   FOOT   FOB   BACH 
AN  INCH. 


OF 


Inch. 

0" 

1" 

2" 

3" 

r 

5" 

0 

0 

.0833 

.1667 

.2500 

.3333 

.4167 

ft 

.0013 

.0846 

.1680 

.2513 

.3346 

.4180 

0026 

.0859 

.1693 

.2626 

.3359 

.4193 

ft 

.0039 

.0872 

.1706 

.2539 

.3372 

.4206 

iV 

.OO52 

.0885 

•  1719 

.2552 

.3385 

.4219 

A 

.0085 

.0898 

.1732 

.2565 

.3398 

.4232 

.0078 

.0911 

.1745 

.2578 

.3411 

.4245 

ei 

.0091 

.0924 

.1768 

.2591 

.3424 

.4258 

1 

.0104 

.0937 

.1771 

.2604 

.3437 

.4271 

ft 

.0117 

.0951 

.1784 

.2617 

.3451 

.4284 

A 

.0130 

.0964 

.1797 

.2630 

.3464 

.4297 

H 

.0143 

.0977 

.1810 

.2643 

.3477 

.4310 

.0156 

.0990 

.1823 

.2656 

.3490 

.4323 

if 

.0169 

.1003 

.1836 

.2669 

.3503 

.4336 

7*2 

.0182 

.1016 

.1849 

.2682 

.3516 

.4349 

ef 

.0195 

.1029 

.1862 

.2695 

.3529 

.4362 

i 

.0208 

.1042 

.1875 

.2708 

.3542 

.4375 

iJ 

.0221 

.1055 

.1888 

.2721 

.3555 

.4388 

A 

.0234 

.1038 

.1901 

.2734 

.3568 

.4401 

if 

.0247 

.1081 

.1914 

.2747 

.3581 

.4414 

.0260 

.1094 

.1927 

.2760 

.3594 

.4427 

H 

.0273 

.1107 

.1:940 

.2773 

.3607 

.4440 

ii 

.0286 

.1120 

.1953 

.2786 

.3620 

.4453 

ft 

.0299 

.1133 

.1966 

.2799 

.3633 

.4466 

Y 

.0312 

.1146 

.1979 

.2812 

.3646 

.4479 

if 

.0326 

.1159 

.1992 

.2826 

.3659 

.4492 

13 

.0339 

.1172 

.2005 

.2839 

.3672 

.4505 

II 

.0352 

.1185 

.2018 

.2852 

.3685 

.4518 

ft 

.0365 

.1198 

.2031 

.2865 

.3698 

.4531 

II 

.0378 

.1211 

.2044 

.2878 

.3711 

.4544 

15 

.0391 

.1224 

.2057 

.2891 

.3724 

.4557 

II 

.0404 

.1237 

.2070 

.2904 

.3737 

.4570 

i 

.0417 

.1250 

.2083 

.2917 

.3750 

.4583 

USEFUL  TABI/ES. 


203 


DECIMALS  OF    A   FOOT   FOR    EACH 
AN   INCH 


OP 


.Inch. 

.6" 

7" 

8' 

P  " 

10" 

11" 

0 

5000 

6833 

.6667 

7500 

.8333 

.9167 

I 

.6013 
.5026 
.5039 
.5052 

.5846 
5859 
5872 
.6885 

.6680 
.6693 
.6706 
.6719 

.7513 
.7526 
.7539 
.7652 

.8346 
.8359 
.8372 
.8386 

.9180 
.9193 
.9206 
.9219 

s 

A 

.5065 
.5078 
.6091 
.5104 

.5898 
.5911 
.5924 
5937 

.6732 
.6746 
.6768 
.6771 

.7665 
.7578 
.7591 
.76O4 

.8398 
.8411 
.8424 
.8437 

.9232 
.9245 
.9258 
,9271 

£ 

1 

A 

.5117 
-6130 
•5143 
.6156 

.5951 
.6964 
.5977 
.5990 

.6784 
.6797 
.6810 
.6823 

.7617 
.7630 
.7643 
.7656 

.8451 
.8464 
.8477 
.8490 

.9284 
.9297 
.931O 
.9323 

S 

ti 

.5169 
5182 
.5195 
.5208 

.6003 
.6016 
.6029 
.6042 

.6836 
.6849 
.6862 
.6875 

.7669 
.7682 
.7695 
.7708 

.8503 
.8516 
.8529 
.8542 

.9336 
.9349 
.9362 
.9375 

H 
H 

| 

.5221 
.5234 
.6247 
.5260 

.6055 
.6068 
.6081 
.6094 

.6888 
.6901 
.6914 
.6927 

.7721 
.7734 
.7747 
.7760 

.8555 
.8568 
.8581 
.8594 

.9388 
.9401 
.9414 
.9427 

fi 
H 

.5273 
.5286 
.5299 
.5312 

.6107 
.6120 
,6133 
.6146 

.6940 
.6953 
.6966 
.6979 

.7773 
.7786 
.7799 
.7812 

.86O7 
.8620 
.8633 
.8646 

.9440 
.9453 
.9466 
.9479 

H 

1 

.5326 
.5339 
.5352 
.5365 

.6159 
.6172 
.6185 
.6198 

.6992 
.7005 
.7018 
.7031 

,7826 
.7839 
,7852 
.7865 

.8659 
.8672 
.8685 
.8698 

.9492 
.9505 
.9618 
.9531 

H 

H 

? 

.5378 
.5391 
.5404 
.5417 

.6211 
.6224 
.6237 
.6250 

.7044 
.7057 
.7070 
.7083 

.7878 
.7891 
.7904 
.7917 

.8711 
.8724 
.8737 
.8750 

.9544 
.9567 
.9670 
.9583 

204 


TABLES. 


DEOTMATtS  OF  A  FOOT  FOB  BACH 
AN  INCH. 


OF 


Inch. 

0 

1" 

2" 

3" 

4" 

5" 

|| 

.0430 

.1263 

.2098 

.2930 

.3763 

,4596 

.0443 

.1276 

.2109 

.2943 

.3776 

,4609 

ff 

.0458 

.1289 

.2122 

.2956 

.3789 

.4622 

ft 

.O469 

.1302 

.2135 

.2969 

.3802 

.4635 

81 

.0482 

.1315 

.2148 

.2982 

.3815 

.4648 

T! 

.0495 

.1328 

.2161 

.2995 

.3828 

.4661 

fi 

.0508 

.1341 

.2174 

.3008 

.3841 

.4674 

,i 

.0521 

.1354 

.2188 

.3021 

.3854 

.4688 

.0534 

.1367 

.2201 

,3034 

.3867 

.4701 

.0547 

.1380 

.2214 

.3047 

.3880 

.4714 

.0560 

.1393 

.2227 

.3060 

.3893 

.4727 

• 

.0573 

.1406 

.224O 

.3073 

.3908 

.4740 

£i. 

.0586 

.1419 

.2253 

.3086 

.3919 

.4753 

$]• 

.0599 

.1432 

.2263 

.3099 

.3932 

.4766 

4J; 

.0612 

.1445 

.2279 

.3112 

.3945 

.4779 

f 

.0825 

.1458 

.2292 

.3125 

.3958 

.4792 

.0638 

.1471 

.2305 

.3138 

.3971 

.4805 

.0651 

.1484 

.2318 

.3151 

.3984 

.4818 

.0664 

.1497 

.2331 

.3164 

.3997 

.4831 

.0677 

.1510 

.2344 

.3177 

.4010 

.4844 

£i 

.0690 

.1523 

.2367 

.3190 

.4023 

.4857 

27 

.O703 

.1536 

.2370 

.3203 

.4036 

.4870 

55 

.O716 

.1549 

.2383 

.3216 

.4049 

.4883 

i 

.0729 

.1562 

.2396 

.3229 

•4062 

•4896 

.0742 

.1576 

.2409 

.3242 

.4076 

.4909 

.0755 

.1589 

.2422 

.8255 

.4089 

.4922 

.0768 

.1602 

.2435 

.326* 

.4102 

,4935 

.0781 

.1615 

.2448 

.3281 

.4115 

.4948 

.0794 

.1628 

.2461 

,3294 

.4128 

.4961 

.0807 

.1641 

.2474 

.3307 

.4141 

.4974 

.0820 

.1654 

.2487 

.3320 

.4154 

.4987 

1 

USEFUL,  TABLES. 


205 


DECIMATE  OP  A   FOOT  FOB  EACH 

AN  INCH. 


OP 


Inch. 

6" 

7" 

8" 

9" 

10" 

11" 

.9596 

.9609 
.9622 
.9635 

1 

.5430 
.6443 
.5456 
.5469 

.6263 
.6276 
.6289 
.6302 

.7096 
.7109 
.7122 
.7135 

.7930 
.7943 
.7966 
.7969 

.8763 

.8776 
.8789 
.8802 

1 

.5482 
.5495 
.5508 
.5521 

.6316 
.6328 
.6341 
.6364 

.7148 
.7161 
.7174 
.7188 

.7982 
.7995 
.8008 
.8021 

.8815 
.8828 
.8841 
.8854 

.9648 
.9661 
,9674 
.9688 

B 

8 

.5534 
.6547 
5560 
.5573 

6367 

.6380 
.6393 
,6406 

.7201 
,7214 
.7227 
.7240 

.8034 
.8O47 
.806O 
.8073 

.8867 
.8880 
.8893 
.8906 

.9701 
.9714 
.9727 
.9740 

1 

.6586 
.5599 
.5612 
.5625 

.6419 
6432 
.6445 
.6458 

.7253 
7266 
.7279 
.7292 

.8086 
.8099 
8112 
.8125 

.8919 
.8932 
.8945 
8958 

.9753 
.9766 
9779 
9792 

II 
ff 

5638 
.5651 
5664 
5677 

.6471 
.6484 
.6497 
6510 

.7306 
.7318 
.7331 
.7344 

.8138 
.8151 
8164 
.8177 

8971 

.8984 
.8997 
.9010 

.9805 
.9818 
.9831 
.9844 

f  • 

.5690 
.5703 
5716 
.5729 

.6523 
.6536 
.6549 
.6562 

.7367 
.7370 
.7383 
.7396 

.8190 
.8203 
.8216 
.8229 

.9023 
.9036 
9049 

.9062 

9857 
.987O 
9883 
.9896 

if 

,5742 
.5755 
.5768 
.5781 

.6576 
.6589 
.6602 
.0615 

.7409 
.7422 
.7435 
.7448 

.8242 
.8255 
.8288 
.8281 

.9076 
.9089 
.9102 
9115 

.9909 
.9922 
.9935 
.9948 

1 

5794 
.5807 
.5820 

.6628 
.6641 
•G654 

.7461 
.7474 
.7487 

.8294 
.8307 
.8320 

.9128 
.9141 
.9154 

.9961 
.9974 
.9987 
1.0000 

2O6 


USEFUI,  TABLES. 


DECIMALS  OP  AN  INCH  FOB,  EACH  fcth. 


TfrJ?. 

V*ths. 

Decimal 

Fraction 

T&&. 

iVfla. 

Decimal. 

Fraction 

1 

.015625 

33 

.515625 

1 

2 

.03125 

17 

34 

,63125 

3 

.O46875 

35 

.546875 

2 

4 

.0625 

1-16 

18 

36 

.5625 

9-16 

5 

.078125 

37 

.678125 

3 

6 

.09376 

19 

38 

.59375 

7 

.IO9375 

39 

.609375 

4 

8 

.125 

1-8 

20 

40 

.625 

5-8 

9 

.140625 

41 

.640625 

6 

1O 

.15625 

21 

42 

.65625 

11 

.171875 

43 

.671875 

6 

12 

.1875 

3-16 

22 

44 

.6875 

11-16 

13 

.203125 

45 

.703125 

7 

14 

.21875 

23 

46 

.71875 

15 

.234375 

47 

.734375 

8 

16 

.25 

1-4 

24 

48 

.75 

3-4 

17 

.265626 

49 

.765625 

9 

18 

,28125 

25 

50 

.78125 

19 

.296875 

51 

.796875 

10 

2O 

.3125 

6-16 

26 

52 

.8125 

13-16 

21 

.328125 

53 

.828125 

11 

22 

.34375 

27 

54 

.84375 

23 

.359375 

55 

.859375 

• 

12 

24 

.375 

3-8 

28 

66 

.875 

7-8 

25 

.390625 

67 

.890625 

13 

26 

,40625 

29 

58 

.90625 

27 

.421875 

59 

.921875 

14 

28 

,4375 

7-16 

3O 

60 

.9375 

15-16 

29 

.453125 

61 

.953125 

15 

30 

.46875 

31 

62 

.96875 

31 

.484375 

63 

.984375 

16 

32 

.5 

1-2 

32 

64 

1. 

1 

USKFUI.  TABLES. 


207 


TABLES   FOR  CALCULATING  THE   HORSE   POWER 
OF  WATER. 


MINERS'  INCH  TABLE. 
The  following  table  gives  the  Horse- 
Power  of  one  miner's  inch  of  water  un- 
der heads  from  one  up  to  eleven  hun- 
dred feet.  This  inch  equals  \%  cubic 
feet  per  minute. 


CUBIC  FEET  TABLE. 
The  following  table  gives  the  Horse- 
Power  of  one  cubic  foot  of  wtiter  pe' 
minute  under  heads  from  one  up  to 
eleven  hundred  feet. 


Heads 
in  Feet. 

Horse  Power 

Heads 
in  Feet. 

Horse  Power. 

He.-ids 
in  Feet. 

HoreePower. 

Heads 
iu  Feet. 

Horse  Power. 

1 

.0024147 

320 

.772704 

1 

.0016098 

320 

.515136 

20 

.0482294 

330 

.796851 

20 

.032196 

330 

.531234 

30 

.072441 

340 

.820998 

30 

.048294 

340 

.547332 

40 

.09(1588 

350 

.84-5145 

40 

.064392 

350 

.563430 

50 

.120735 

360 

.869292 

50 

.080490 

360 

.579528 

06 

.144882 

370 

.898439 

60 

.096588 

370 

.595626 

70 

.169029 

380 

.917586 

70 

.112686 

380 

.G11724 

80 

.193176 

390 

.944733 

SO 

.128784 

390 

.627822 

90 

.217323 

400 

.965880 

90 

.144892 

400 

.643920 

100 

.241470 

410 

.990027 

100 

.1(50980 

410 

.660018 

110 

.265617 

420 

1.014174 

110 

.177078 

420 

.676116 

120 

.289764 

430 

1.038321 

120 

.193170 

430 

.692214 

130 

..S13911 

440 

1.062468 

.130 

.209274 

440 

.706312 

140 

.338058 

450 

1.086615 

140 

.225372 

450 

.724410 

150 

.362205 

460 

1.110762 

150 

.241470 

460 

.740508 

160 

.386352 

470 

1.134909 

160 

.257568 

470 

.75b'600 

170 

.410499 

480 

1.159056 

170 

.273666 

480 

.772704 

180 

.434646 

490 

1.183206 

180 

.289764 

490 

.788802 

190 

.458793 

500 

1.207350 

190 

.305862 

500 

.804900 

200 

.482940 

520 

1.255644 

200 

.321960 

520 

.837096 

210 

.507087 

540 

1.303938 

210 

.338058 

540 

.869292 

220 

.531234 

560 

1.352232 

220 

.354156 

560 

.901488 

230 

.555381 

580 

1.400526 

230 

.370254 

580 

.933684 

240 

.579528 

600 

1.446820 

240 

.386352 

600 

.965880 

250 

.603675 

650 

1.569555 

250 

.402450 

650 

1.046370 

260 

.627822 

700 

1.690290 

260 

.418548 

700 

1.126860 

270 

.651969 

750 

1.811025 

270 

.434646 

750 

1.207350 

280 

.676116 

800 

1.931760 

280 

.450744 

800 

1.287840 

290 

.700263 

900 

2.173230 

290 

.466842 

900 

1.448820 

300 

.724410 

1000 

2.414700 

SCO 

.482940 

1000 

1.609800 

310 

.748557 

1100 

2.656170 

310 

.499038 

1100 

1.770780 

WHEN   THE   EXACT  HEAD  IS  FOUND  IN  ABOVE   TABLE. 

EXAMPLE. — Have  100  foot  head  and  50  inches  of  water.  How  many  Horse- 
Power? 

By  reference  to  above  table  the  Horse  Power  of  r  inch  under  100  ft.  head 
is  .241470.  This  amount  multiplied  by  the  number  of  inches.  50,  will  give  12.07 
Horse  Power. 

WHEN   EXACT  HEAD  IS  NOT  FOUND  IN  TABLE. 

Take  the  Horse  Power  of  i  inch  under  i  ft.  head  and  multiply  by  the  num- 
ber of  inches,  and  then  by  number  of  feet  head.  The  product  will  be  the  required 
Horse  Power. 

The  above  formula  will  answer  for  the  cubic  feet  table,  by  substituting  the 
the  equivalents  therein  for  those  of  miner's  inches. 

NOTE. — The  above  tables  are  based  upon  an  efficiency  of  85%. 


208 


USEFUL, 


LOSS  OF  HEAD  IN  PIPE  BY  FRICTION. 

The  following  tables  show  the  loss  of  head  by  friction  in  each  100  feet  in  length  of  different 
diameters  of  pipe  when  discharging  the  following  quantities  of  water  per  minute: 

INSIDE  DIAMETER  OF  PIPU  IN  INCHES. 


} 

2 

3 

4 

5 

6 

Velo 
inn 
Per 

Loss  of 
head 
in 
feet. 

Cubic- 
feet 
pojr 
mln. 

Loss  of 
head 
in 
feet. 

Cubic 

feet 

mfn 

Loss  of 
he<td 

feet 

Cubic 
feet 
per 
mfu. 

Loss  of 
head 

& 

Cubic 
feet 
per 
min. 

Ixjesof 
head 

feet. 

Cubio 
feet 

mPfnr. 

Lose  of 
head 
in 

feet 

Cubic 
feet 
per 

2.0 

2.87 

.05 

1.185 

2.62 

.791 

5.89 

.593 

10.4 

.474 

16.3 

.395 

23.5 

2.2 

2.80 

.73 

1.404 

2.88 

.936 

6.48 

.*702 

11.5 

.561 

18. 

.468 

25.9 

2.4 

3.27 

.79 

1.639 

3.14 

1.093 

7.07 

.819 

12.5 

.650 

19.6 

.547 

28.2 

2.6 

3.78 

.80 

1.891 

3.40 

1.26 

7.65 

.945 

13.6 

.757 

21.3 

.631 

306 

28 

4.32 

.92 

2.16 

3.66 

1.44 

8.24 

l.OSi 

14.6 

.864 

22.9 

.720 

32.9 

8.0 

4.89 

.99 

2.44 

3.92 

1.62 

8.83 

1.22 

15.7 

.978 

24.5 

.815 

35.3 

8.2 

6.47 

1.06 

2.73 

4.18 

1.82 

9.42 

1,37 

16.7 

1.098 

26.2 

.915 

37.7 

3.4 

6.09 

1.12 

3.05 

4.45 

2.04 

10.00 

1.52 

17.8 

1.22 

27.8 

1.021 

40. 

3.6 

6.76 

1.19 

3.38 

4.71 

2.26 

10.60 

1.69 

18.8 

1.35 

29.4 

1.131 

42.4 

8.8 

7.48 

1.20 

3.74 

4.97- 

2.49. 

11.20 

1.87 

19.9 

1.49 

31. 

1.25 

44.7 

4.0 

8.20 

1.32 

4.10 

5.23 

2.73 

11.80 

2.05 

20.9 

1.64 

32.7 

1^37 

47.1 

4.2 

8.97 

1.39 

4.49 

5.49 

2.98 

12.30 

2,24 

22.0 

1.79 

34.3 

1.49 

49.5 

4.4 

9.77 

1.45 

4.89 

5.76 

3.25 

12.90 

2.43 

23.0 

1.95 

36.0 

1.62 

51.8 

4.6 

10.60 

1.52 

5.30 

6.02 

8.53 

•13.50 

2.64 

24.0 

2.11 

37.6 

1.76 

64.1 

4.8 

ll'.4ft 

1.58 

6.72 

6.28 

3:81 

14.10 

£Bft 

25.1 

2.27 

39.2 

1:90 

56.5 

£.0 

12.33 

1.65 

6.17 

6.54 

4.11 

14.70 

3.08 

26.2 

2.46 

40.9 

2.05 

58.0 

6.2 

13.24 

1.72 

0.62 

6.80 

4.41 

15.30 

331 

•27.2 

2.65 

42.5 

2.21 

61.2 

6.4 

14.20 

1.78 

7.10 

7.06 

4.73 

15.90 

3.55 

28.2 

2.84 

44.2 

2.37 

63.6 

6.0 

15.16 

1.85 

7.58 

7.32 

5.06 

16.50 

3.79 

29.3 

3.03 

45.8 

2.53 

65.9 

6.8 

10.17 

1.91 

8.09 

7.58 

5.40 

17.10 

4.04 

30.3 

3.24 

47.4 

2.70 

68.3 

6.0 

17.23 

1.98 

8.61 

7.85 

5.74 

17.70 

4.31 

31.4 

3.45 

49.1 

2.87 

70.7 

7.0 

22.89 

2.31 

11.45 

9.16 

7.62 

20.6 

6.72 

36.6 

4.57 

57.2 

?.8l 

82.4 

INSIDE  DIAMETER  OF  PIPE  IN  INCHES. 


7 

8 

9 

10 

n 

12 

V«lo 
In  ft. 
per 

aec. 

Low  of 
head 
in 
feet. 

Cubic 
feet 
per 
min. 

LOBBOf 

head 
feet. 

Cubic 
feet 

mtn 

Loss  of 
head 

feet. 

Cubic 
feet 

mtn. 

Loss  of 
head 
in 
feet. 

Cubic 
feet 
per 
miii. 

Loss  of 
head 

feet. 

Cubio 
feet 
per 

Loss  of 
head 
in 
feet. 

Cubic 
feet 

mtn 

2.0 

.338 

32.0 

.296 

41.9 

.264 

53. 

.237 

65.4 

.216 

79.2 

.198 

94.2 

.401 

36.3 

..351 

46.1 

.312 

58.3 

.281 

72. 

.255 

87.1 

.234 

103. 

2.4 

.468 

3S.5 

.410 

50.2 

.365 

63.6 

.327 

78.5 

.297 

95.0 

.273 

113. 

2.6 

.540 

41.7 

.473 

54.4 

.420 

68.9 

.378 

85.1 

.344 

103". 

.315 

122. 

2.8 

.617 

449 

.540 

68.6 

.480 

74.2 

.432 

91.6 

.392 

111. 

.360 

132. 

3.0 

.698 

48.1 

.611 

62.8 

.544 

79.5 

.488 

98.2 

.444 

119. 

.407 

141. 

3.2 

.785 

51.3 

.686 

67. 

.609 

84.8 

.549 

105. 

.499 

127. 

.457 

151. 

8.4 

.876 

54.6 

.765 

71.2 

.680 

90.1 

.612 

111. 

.557 

134. 

,510 

160. 

8.6 

.969 

57.7 

.848 

75.4 

.755 

95.4 

.679 

118. 

.017 

142. 

.566 

169. 

8.8 

Ifl70 

60.9 

.936 

79.6 

.831 

101. 

.749 

124. 

.GSO 

150. 

.624 

179. 

4.0 

1.175 

64.1 

1.027 

83.7 

.913 

106. 

.822 

131. 

.747 

158. 

.685 

188. 

4.2 

1.28 

67.3 

1,122 

87.9 

.998 

111. 

.897 

137. 

.816 

166. 

.749 

198. 

4.4 

1.39 

70.5 

1.22 

92,1 

1.086 

116. 

.977 

144. 

.888 

174. 

.815 

207. 

4.6 

1.51 

73.7 

1.32 

98.3 

1.177 

122. 

1.059 

160. 

.903 

182. 

.883 

217. 

4.8 

IJ&S 

76.9 

1.43 

100.0 

1.27 

127. 

1.145 

157. 

1.040 

190. 

.954 

226 

5.0 

J.76 

80.2 

1.54 

105. 

1.37 

132. 

1.23 

163. 

1.122 

198. 

1.028 

235. 

6.2 

1.89 

83.3 

1.65 

109. 

1.47 

138. 

1.32 

170. 

1.20 

206. 

1.104 

245 

64 

2.03 

8(5.6 

1.77 

113. 

1.57 

143. 

1.41 

177. 

1:28 

214. 

1.183 

254. 

6.6 

2.17 

89.8 

1.89 

117. 

1.6S 

148. 

1.51 

183. 

1.37 

222. 

1.26 

264. 

6.8 

2.31 

93.0 

2.01 

121. 

1.80 

154. 

1.61 

190. 

1.46 

229. 

134 

273. 

6.0 

2.46 

96.2 

2.15 

125. 

1.92 

159. 

1.71 

196. 

1.56 

237. 

1.43 

283. 

7.0 

3.2fi 

112.0 

2.85 

140. 

2.52 

185. 

2.28 

229. 

2.07 

277. 

1.91 

S30, 

U3SFUI,  TABLES. 


209 


LOSS  OF  HEAD  IN  PIPE  BY  FRICTION. 

The  following  tables  show  llio  loss  of  head  by  friction  in  each  100  feet  in  length  of  diflerenl 
diameters  of  pipe  when  discharging  the  following  quantities  of  water  per  mirute : 

INSIDE  DIAMETER  OF  PIPE  IN  INCHES. 


1 

3 

1 

4 

1 

5 

1 

6 

1 

3 

j 

0 

V«1o 

Loss  of 

Cubto 

Low  of 

Cublo 

Loss  of 

Cubic 

Lossof 

Cublo 

Lossof 

Cubic 

Lossof 

Cubic 

in  ft 

head 

feet 

head 

feet 

head 

feet 

head 

feet 

head 

ffcet 

hca<l 

llH't 

per 

flnt 

mi" 

m 

mhL 

per 

In 

mfn. 

In 

PIT 

=• 
2-0 

•msssss 
.183 

- 
110. 

J—  —  .' 
.169 

128. 

fee 
.158 

into 
147. 

feet 
.147 

167. 

.132 

- 
212. 

." 
.119 

"TT 

2.2 

.216 

m. 

.200 

141. 

.187 

162. 

.175 

184. 

.156 

233. 

.140 

28S." 

2.4 

.252 

133. 

.234 

154. 

.218 

176. 

.205 

201. 

.182 

254. 

.164 

314. 

2.6 

.290 

144. 

.270 

167. 

.252 

191. 

.236 

218. 

.210 

275. 

.189 

340. 

2.8 

.332 

158. 

.308 

179. 

.288 

206. 

,270 

234. 

.240 

297. 

.216 

366. 

30 

.375 

166. 

.349 

192. 

.325 

221. 

.306 

251. 

.271 

318. 

.245 

393. 

3.2 

.422 

177. 

.392 

205. 

.366 

235. 

.343 

268. 

.305 

339. 

.275 

419. 

3.4 

.471 

188. 

.433 

218. 

.408 

250. 

.383 

284. 

.339 

360. 

.306 

445. 

J.6 

.522 

199. 

.485 

231. 

.452 

265. 

.425 

301. 

.377 

382. 

.339 

471. 

3.8 

.576 

210. 

.535 

243. 

.499 

280. 

.468 

318. 

.416 

403. 

.374 

497. 

4.0 

.632 

221. 

.587 

256. 

.543 

294. 

.513 

335. 

.456 

424. 

.410 

523. 

4.2 

.691 

232. 

.641 

269. 

.598 

309. 

.561 

352. 

.499 

445. 

.449 

550. 

4.4 

.751 

243. 

.698 

282. 

.651 

324. 

.611 

368. 

.542 

466. 

.488 

576. 

4.6 

.815 

254. 

.757 

295. 

.707 

339. 

.662 

385. 

.588 

488. 

.529 

602. 

4.8 

.881 

265. 

.818 

308. 

.763. 

353. 

.715 

402. 

.636 

509. 

.572 

628. 

5.0 

.949 

276. 

.881 

321. 

.822 

368. 

.770 

419. 

.685 

530. 

.617 

654. 

5.2 

1.020 

287. 

.947 

333. 

.883 

383. 

.828 

435. 

.736 

551. 

.662 

680. 

5.4 

1.092 

298. 

1.014 

346. 

.947 

397. 

.888 

452. 

.788 

572. 

.710 

707. 

6.6 

1.167 

309. 

1.083 

359. 

1.011 

412. 

.949 

169. 

.843 

594. 

.758 

733. 

5.8 

1.245 

821. 

1.155 

372. 

1078 

427. 

1.011 

486. 

.899 

615. 

.809 

759.- 

6.0 

1.325 

332. 

1.229 

385. 

1.148 

442. 

1.076 

502. 

.957 

636. 

.861 

785. 

7.0 

1.75 

387. 

1.43 

449. 

1.52 

515. 

1.43 

586. 

1.27 

742. 

1.143 

916. 

INSIDE  DIAMETER  OF  PIPE  IN  INCHES. 


22 

21 

26 

28 

30 

36 

Vein. 

Lossof 

Cubic 

Lossof 

Cubic 

Lossof 

Cubic 

Lossof 

Cubic 

Lossof 

Cubic 

I-ossof 

Cubic 

ill  fl. 

head 

fec-t 

head 

feet 

bead 

f«et 

head 

feet 

head 

feet 

head 

feet 

per 

per 

per 

in 

per 

in 

per 

in 

per 

in 

per 

sec. 

feet. 

min. 

feet. 

min. 

feet. 

feet 

/min. 

feet. 

min. 

feet. 

2.0 

.108 

316. 

.098 

377. 

J091 

442. 

.084 

513. 

.079 

589. 

.0(H5 

848. 

2.2 

.127 

348. 

.116 

414. 

.108 

486. 

.099 

564. 

.093 

648. 

.C78 

2.4 

.149 

380. 

.136 

452. 

.126 

531. 

.116 

616. 

.109 

707. 

.091 

iois! 

2.6 

.171 

412. 

.157 

490. 

.145 

575. 

.134 

667. 

.126 

766. 

.104 

1100. 

2.8 

.195 

443. 

.180 

52». 

.165 

619. 

.i53 

718. 

.144 

824. 

.119 

1188. 

3.0 

.222 

475. 

.204 

565. 

.188 

663. 

.174 

770. 

.163 

883. 

.135 

1273. 

3.2 

.249 

507. 

.229 

603. 

.211 

708. 

.195 

821. 

.182 

942. 

.1*2 

1357. 

3.4 

.273 

538. 

.255 

641. 

.235 

752. 

.218 

872. 

.204 

•ICO  I. 

.169 

1442. 

3.6 

.308 

57p. 

.283 

678. 

.261 

796. 

.242 

923. 

.226 

1060. 

.188 

1527. 

3.8 

.340 

601. 

.312 

716. 

.288 

840. 

.267 

974. 

.249 

1)19. 

.207 

1612. 

4.0 

.373 

633. 

.342 

754. 

.315 

885. 

.293 

1026. 

.273 

1178. 

.228 

1697. 

4.2 

.408 

665. 

.374 

791. 

.345 

929. 

.320 

1077. 

.299 

1237. 

.249 

1782. 

4.4 

.444 

697. 

.407 

829. 

.375 

973. 

.348 

1129. 

.325 

1296. 

.271 

1866. 

4.6 

.482 

728. 

.441 

867. 

.407 

1017. 

.378 

1180. 

.353 

1355. 

.294 

195JL 

4.8 

.621 

760. 

.476 

905. 

.440 

1062. 

.409 

1231. 

Ml 

1414. 

.318 

203«. 

6.0 

.561 

792. 

.513 

942. 

.474 

1106. 

.440 

1283. 

.411 

1472. 

.312 

2121.. 

62 

.602 

823. 

.552 

980. 

.510 

1150. 

.473 

1334. 

.441 

1531. 

.368 

2206.. 

6.4 

.645 

855. 

.591 

1018: 

.546 

1194. 

.507 

1885. 

.473 

1590. 

.394 

2291. 

6.6 

.690 

887. 

.632 

1055. 

.583 

1239. 

.542 

1437. 

.506 

1649. 

.421 

2376. 

6.8 

.735 

918, 

.674 

1093, 

.622 

1283. 

.578 

1488. 

.540 

1708. 

.450 

2460. 

6.0 

.782 

950. 

.717 

1131. 

.662 

1327. 

.615 

1539. 

.574 

1767. 

.479 

2545. 

7.0 

1.040 

1109. 

.953 

1319. 

.879 

1548. 

.817 

1796. 

.762 

2061. 

.636 

2S68. 

210 


TABLES. 


TABLE  OF  SHEET  IRON  HYDRAULIC  PIPE, 


I  a 

3 

4 

4_ 

5~ 

5 


8 
8 
8 

~V 
9 

_JL 

10 

10 

10 
10 
10 

11 
11 

31 
11 
11 
12 
12 
12 
12 
12 
13 
13 
13 
13 

JJL 
14 
14 
14 
14 

_1£ 
15 
15 
15 
15 

_15_ 
16 
16 
36 
16 


Area  of  pipe  in 
inches. 

Thickn'sof  iron 
by  wire  gauge. 

Head  in  feet  the 
pipe  will  safely 
stand. 

Cub.  ft.  of  water 
pipe  will  convey 
per  min.  at  vel. 
3  ft.  per  second. 

Weight  per  line- 

Al  foot  In  Ihs. 

Diameter  of  pipe 
in  inches. 

Area  of  pipe  in 
inches. 

Thickn'sof  iron 
by  wire  gauge. 

C  0% 

•S3 

8* 

33  Q-5 
W5.S 

Cub.  ft.  of  water1 
pipe  will  convey 
per  mim  at  vel. 
3  ft.  persecond^ 

Weight  per  line- 
al foot  iu  Jbs. 

7 
12 
12 
•JO 
20 

18 
18 
16 
18 
16 

400 
350 
525 
325 
500 

9 
16 
16 
25 
25 

2 

1 
; 

18 
L   18 
18 

F  18 

.18 

254 
254 
254. 
254 
254 

10 
14 
12 
11 
10 

165 
252 
385 
424 
505 

320 
320 
320 
320 
320 

16* 
20* 
27j 
30 
34 

20 

14 

675 

25 

5 

f  "20 

314 

16 

148 

400 

18 

28 
28 
28 

—  w~ 

18 
16 
14 
18 

296 

4S7 
743 

9~»J. 

36 
36 
36 

ei\ 

4 
5 

n 

c 

,   20 
i   20 
<   20 
L  20 

314 
314 
314 

14 
12 
11 
10 

22  / 
346 
380 
456 

400 
400 
400 

224 
80 
32* 

ml 

38 

38 

16 
14 

419 
640 

50 

50 

ft 

i 

,   22 
22 
22 

380 
380 
380 

16 
14 
12 

135 

206 
316 

4SO 
480 
480 

20 

Sf 

50 
50 
50 

16 
14 

19 

367 
560 

OKA 

s 

63 

% 

1  Q 

>   22 
22 

380 
380 

H 
10 

347 
415 

480 
480 

S1 

24 

452 

14 

188 

670 

27  J. 

63 
63 
63 

16 
14 
12 

327 
499 
761 

80 
80 
80 

8 
IQ\ 
14 

24 
24 
24 

452 
452 
452 

12 
11 
10 

290 
318 
379 

570 
570 
570 

35* 
39 

43* 

78 

16 

295 

100 

9 

24 

452 

8 

466 

570 

53 

78 
78 
78 
78 

14 
12 
11 
10 

450 
687 
754 
900 

100 
100 
100 
100 

11} 
15 
17 
19 

26 
26 
26 
^   26 

530 
530 
530 
530 

14 
12 
11 
10 

175 
267 
294 
352 

670 
670 
670 
670 

29* 
384 
42" 
47 

95 

16 

269 

120 

9i 

26 

530 

8 

432 

670 

57} 

95 
95 
95 
95 

14 
12 
11 
10 

412 
626 
687 
820 

120 
120 
120 
120 

13 

17} 

i«i 

21 

28 

r   28 
28 
.  28 

615 
615 
615 
615 

14 
12 
11 
10 

102 
247 
273 
327 

775 
775 
775 
775 

31} 
41} 
45 

50} 

113 

16 

246 

142 

11 

28 

615 

8 

400 

775 

61} 

113 
113 
113 
113 

14 
12 
11 
10 

377 
574 
630 
753 

142 
142 
142 
142 

14 
18j 
19 
22| 

30 
30 
30 
30 

706 
706 
706 
706 

12 
11 
10 

8 

231 

254 
304 
375 

890 
890 
890 
890 

44 
48 
54 
65 

132 

16 

228 

170 

12 

30 

706 

i 

425 

890 

74 

132 
132 
132 
132 

14 
12 

11 
J0_ 

348 
530 
583 
696 

170 
170 
170 
170 

15 

20 
22 
_24j 

33 
3J 
36 
-,  36 

1017 
1017 
1017 
1017 

11 
10 

8 

7 

141 
155 
192 
210 

1300 
1300 
1300 
1300 

58 
67 

78 
88 

153 
153 
153 
153 

14 
12 
11 
10 

324 

494 
543 
648 

200 
200 
200 
200 

16 

Si 

*6 

40 
t   40 
40 
40 

1256 
1256 
1256 
1256 

10 
8 
7 
6 

141 
174 
189 
213 

1600 
1600 
1600 
1600 

71 
86 
97 
108 

1  9fi 

176 

16 

197 

225 

ISj 

-   40 

176 
176 
176 
176 

14 
12 
11 

10 

302 
46U 
507 
606 

225 
225 
225 
225 

17 
23 

24: 
28 

42 
42 

t   42 
42 

1385 
1385 
1335 
1385 

10 

8 
7 
6 

135 
165 
180 
210 

1760 
1760 
1760 
1760 

74$ 

a 

102 
114 

201 
201 
201 
201 
201 

16 
14 
12 
11 

10  J 

185 
283 
432 
474 
5(57 

255 
255 
255 
255 
255 

14 
IT 
24 
26 
29^ 

r  42 

42 
.   42 
42 

k   42 

13H5 
1385 
1385 
1385 
1385 

4 

3 
A 

240 
270 
300 
321 
363 

1760 
1760 
17t>0 
1760 
.  1760 

133 
137 
145 
177 
216 

;  USEKJI,  TABLES. 


211 


fl 

rt 

rO 

-T 

- 

0 

+ 

CO 

N 

CO 

00 

00 

00 

- 

CO 
N 

0 

si 

\ 

*  j 

•T. 

0, 

SO 

N 

<3~ 

•, 

rO 

(o 

N 

rV 

K 

\0 

\T 

rV 

§\ 

0 

0 

0 

0 

* 

— 

- 

- 

H 

c^ 

"> 

rO 

T 

<o 

jM 

'  2 

N 

00 

vT 

0 

•1 

X> 

«0 

0 

<0 

5 

^ 

0 

o 

0 

t 

> 

^'*- 

<r 

^ 

^O 

^o 

<o 

If) 

<o 

vo 

vo 

r^ 

N 

«5 

cr 

0 

1 

i 

r 

M 

1 

•f 

M 

t 

^ 

• 

c 

«o 

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•0 

^ 

o 

xO 

O 

^ 

^ 

^ 

^ 

00 

5. 

oo 

_. 

v/ 

> 

* 

o 

<J- 

N. 

0 

r*) 

<o 

00 

0 

^ 

-5- 

si 

rs. 

13- 

o 

rV 

>„ 

1 

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vfl 

00 

CO 

03 
OS 

0 

<r 

o- 

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fO 

<r 

cr 

cr 

€0 

tr> 

cr 

0 

r, 

0 

10 

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ri 

^"u- 

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r( 

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^ 

5  N» 

lu 

s 

fl 

rfl 

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0 

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00 

S" 

0 

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5 

* 

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<b 

s7 

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I 

3         ^  i/7 

(< 

^> 

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L. 

J  *  ^*_fi  : 

il 

N 

sQ 

(t 

rO 

0 

rO 
N 

•x 

00 

5 

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212 


TABLES. 


The  following  is  a  very  useful  table  and  should  be  employed 
in  Compressed  Air  distribution.  The  efficiency  of  many  plants 
would  be  increased  if  the  piping  followed  these  proportions: 

Equation  of  Pipes*— It  is  frequently  desired  to  know  what  number 
of  pipes  of  a  given  size  are  equal  in  carrying  capacity  to  one  pipe  of  a  larger 
size.  At  the  same  velocity  of  flow  the  volume  delivered  by  tieo  pipes  of 
different  sizes  is  proportional  to  the  squares  of  their  diameters;  thus,  one 
4-inch  pipe  will  deliver  the  same  volume  as  four  2-iuch  pipes.  With  the  same 
head,  however,  the  velocity  is  less  in  the  smaller  pipe,  and  the  volume  de- 
livered varies  about  as  the  square  root  of  the  fifth  power  (i.e.,  as  the  to. 5 
power).  The  following  table  has  been  calculated  on  this  basis.  The  figures 
opposite  the  intersection  of  any  two  sizes  is  the  number  of  the  smaller-sized 
pipes  required  to  equal  one  of  the  larger.  Thus,  one  4-inch  pipe  is  equal  to 
5.7  2  inch  pipes. 


is 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

12 

14 

16 

18 

20 

24 

2 

5.7 

1 

3 

15.6 

2.8 

1 

4 

32 

5.7 

2.1 

1 

5 

55.9 

9.9 

3.6 

1.7 

1 

6 

88.2 

15.6 

5  7 

2.8 

1.6 

1 

7 

130 

22.9 

8  3 

4.1 

2.3 

1.5 

1 

8 

181 

32 

11.7 

5.7 

3.2 

2.1 

1.4 

1 

9 

243 

43. 

15.6 

7.6 

4.3 

2.8 

1.9 

1.3 

1 

10 

316 

55.9 

20.3 

9.9 

5.7 

3.6 

2.4 

1.7 

13 

1 

11 

401 

70.9 

25.7 

12.5 

7.2 

4.6 

3.1 

2.2 

1.7 

1.3 

499 

88.2 

32 

15.6 

8.9 

5.7 

3  8 

2.8 

2.1 

1.6 

I 

13 

609 

108 

39.1 

19 

10.9 

7  1 

4.7 

3.4 

2.5 

1.9 

1.2 

14 

733 

130 

47 

22.9 

13.1 

8^3 

5.7 

4.1 

3.0 

2.3 

1.5 

15 

787 

154 

55.0 

27.2 

15.6 

9.9 

6.7 

4.8 

3.6 

2.8 

1.7 

.2 

16 

181 

&5.7 

32 

18.3 

11.7 

7.9 

5.7 

4.2 

3.2 

o  i 

.4 

17 

211 

76.4 

37.2 

21.3 

13.5 

9.2 

6.6 

4.9 

3.8 

2.4 

.6 

.2 

18 

243 

88.  x> 

43 

24.6 

15.6 

10  6 

7  fi 

5.7 

4.3 

2.8 

.9 

.3 

1 

19 

278 

101 

49.1 

28.1 

17.8 

12.1 

8.7|  6.5 

5 

3.2 

2.1 

5 

1.1 

20 

316 

115 

55.9 

32 

20.3 

13  8 

9.9 

7.4 

5.7 

3.6 

2.4 

7 

1.3 

1 

22 

401 

146 

70.9 

40.6 

25.7 

17.5 

12.5 

9.3 

7.2 

4.6 

3.1 

2.2 

1.7 

1.3 

24 

109 

181 

88.2 

50.5 

32 

21.8 

15.6 

11.6 

8.9 

5.7 

3  8 

2.8 

2.1 

1.6 

1 

26 

609 

108 

61.7 

39.1 

26.6 

19. 

14.2 

10.9 

7.1 

4.7 

3.4 

2.5 

1.9 

1.2 

28 

733 

266 

130 

74.2 

47 

32 

22.9 

17  1 

13.1 

8.3 

5.7 

4,1 

3 

2.3 

1.5 

30 
36 

787 

316 
109 

154 
243 

88.2 
130 

55.9 
88.2 

38 
60 

','7.2 
43 

20.3 

32 

15.6 
24.6 

9.9 

15.6 

6.7 
10.6 

4.8 
7.6 

3.o 
5.7 

2.8 
4.3 

1.7 

2.8 

42 

T33 

357 

205 

130 

88.2 

63.2J47 

36.2  19 

15.6 

11.2 

8.3 

6.4 

4  'i 

48 

499 

286 

181 

123 

88.2 

62.7 

50.5 

32 

21.8 

15.6 

11.6 

8.9 

5.7 

54 
60 

670 

78? 

383 
499 

243 
316 

165 
215 

118  188.2 
154  1115 

67.8 

88.2 

43 
55.9 

25.2 
38 

20.9 
27.2 

15.612 
20.315.6 

7.6 
9.9 

USEFUL 


213 


Used  in  the  calculation  of  problems  in  Isothermal  Compres- 
sion and  Expansion  of  Compressed  Air. 

HYPERBOLIC    LOGARITHMS. 


No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

1.01 

.0099 

.45 

.3716 

.89 

,6366 

2.33 

.8458 

2.77 

.0188 

1.03 

.0198 

.46 

.3784 

.90 

.6419 

2.34 

.8502 

2.78 

.0225 

1.03 

.0296 

.47 

.3853 

.91 

.6471' 

2.35 

.8544 

2.79 

.0260 

1.04 

.0392 

.48 

.3920 

.92 

.6623 

2.36 

.8587 

2.80 

.0296 

1.05 

.0488 

.49 

.3988 

|  .93 

.6575 

2.37 

.8629 

2.81 

.0332 

1.06 

.0583 

.50 

.4055 

.94 

.6627 

2.38 

.8671 

2.82 

.0367 

1.07 

.0677 

.51 

.4121 

.95 

.6678 

2.39 

.8713 

2.83 

.0403 

1.08 

.0770 

.52 

.4187 

.96 

.6729 

2.40 

.8755 

2.84 

.0438 

1.09 

.0862 

.53 

.4253 

.97 

.6780 

2.41 

.8796 

2.85 

.0473 

1.10 

.0953 

.54 

.4318 

.98 

.6831 

2.42 

.8838 

2.86 

.0508 

1.11 

.1044 

.55 

.4383 

.99 

.6881 

2.43 

.8879 

2.87 

.0543 

1.12 

.1133 

.56 

.4447 

2.00 

.6931 

2.44 

.8920 

2.88 

.0578 

1.13 

.1222 

.57 

.4511 

2.01 

.6981 

2.45 

.8961 

2.89 

.0613 

1.14 

.1310 

.58 

.4574 

2.02 

.7031 

2.46 

.9002 

2.90 

.0647 

1.15 

.139a 

.59 

.4637 

2.03 

.7080 

2.47 

.9042 

2.91 

.0682 

1.16 

.1484 

.60 

.4700 

2.04 

.7129 

2.48 

.9083 

2.92 

.0716 

1.17 

.1570 

.61 

.4762 

2.05 

.7178 

2.49 

.9123 

2.93 

.0750 

1.18 

.1655 

.62 

.4824 

2.06 

.7227 

2.50 

.9163 

2.94 

.0784 

1.19 

.1740 

.63 

.4886 

2.07 

.7275 

2.51 

.9203 

2.95 

.0813 

1.20 

.1823 

.64 

.4947 

2.08 

.7324 

2.52 

.9243 

2.96 

.0852 

1.21 

.1906 

.65 

.5008 

2.09 

.7372 

2.53 

.9282 

2.97 

.0886 

1.22 

.1988 

.66 

,5068 

2.10 

.7419 

2.54 

.9322 

2.98 

.0919 

1.23 

.2070 

.67 

.5128 

2.11 

.7467 

2.55 

.9361 

2.99 

.0953 

1.24 

.2151 

.68 

.5188 

2.12 

.7514 

2.56 

.9400 

3.00 

.0986 

1.25 

.2231 

.69 

.5247 

2.13 

.7561 

2.57 

.9439 

3.01 

.1019 

1.26 

.2311 

.70 

.5306 

2.14 

.7608 

2.58 

.9478 

3.02 

.1053 

1.27 

.2390 

.71 

5365 

2.15 

.7655 

2.59 

.9517 

3.03 

.1086 

1.28 

.2469 

.72 

.5423 

2.13 

.7701 

2.60 

.9555 

3.04 

.1119 

1.29 

.2546 

.73 

.5481 

2.17 

.7747 

2.61 

.9594 

3.05 

.1151 

1.30 

.2624 

,74 

.5539 

2.18 

.7793 

2.62 

.9632 

3.06 

.1184 

1.81 

.2700 

•75 

.5596 

2.19 

.7839 

2.63 

.9670 

3.07 

.1217 

1.32 

.2776 

.76 

.5653 

2.20 

.7885 

2.64 

.9708 

3.08 

.1249 

1.33 

.2852 

.77 

.5710 

2.21 

.7930 

2.65 

.9746 

3.09 

.1282 

1.34 

.2927 

.78 

.5766 

2.22 

.7975 

2.66 

.9783 

3.10 

.1314 

1.35 

.3001 

.79 

,5822 

2.28 

.8020 

2.67 

.9821 

3.11 

.1346 

1.36 

.3075 

.80 

.5878 

2.24 

.8065 

2.68 

.9858 

3.12 

.1378 

1.37 

.3148 

.81 

.5933 

2.25 

,8109 

2.69 

.9895 

8.13 

.1410 

1  '8 

.3221 

.82 

.5988 

2.26 

.8154 

2.70 

.9933 

3.14 

.1442 

1.33 

.3293 

.83 

.6043 

2.27 

.8198 

2.71 

.9969 

3.15 

.1474 

?.40 

.3365 

.84 

.6098 

2.28 

.8242 

2.72 

1.0006 

3  16 

.1506 

1.41 

.3436 

.85 

.6152 

2.29 

.8286 

2.73 

1.0043 

3.17 

.1537 

1.42 

.3507 

.86 

.<>206 

2.30 

.a329 

2.74 

1.0080 

3.18 

J.1569 

1.43 

.a577 

.87 

.6-.>59 

2.31 

.8372 

2.75 

1.0116 

3.19 

1.1600 

1.44 

.3646 

1.88 

.6313 

2,32 

-8410 

2.76 

1.0152 

3.20 

1.1632 

214 


HYPERBOLIC  LOGARITHMS. 


No.. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

No. 

Log. 

3.21 

.1663 

3.87 

.3533 

4.53 

1.5107 

5.19 

1.6467 

5.85 

1.7664 

3.22 

.1694 

3.88 

.3558 

4.54 

1.5129 

5.20 

1.6487 

5.86 

1  .7681 

3.23 

.1725 

3.89 

.3584 

4.55 

1.5151 

5.21 

.6506 

5.87 

.7699 

3.24 

.1756 

3.90 

.3610 

4.56 

.5173 

5.22 

.6525 

5.88 

.7716 

3.25 

.1787 

3.91 

.3635 

4.57 

.5195 

5.23 

.6514 

5.89 

.7733 

3.26 

.1817 

3.92 

.3661 

4.5S 

.5217 

5.24 

.6563 

5.90 

.7750 

3.27 

.1848 

3.93 

.3686 

4.59 

.5239 

5.25 

.6582 

5.91 

•  .7766 

3.28 

.1878 

3.94 

.3712 

4.60 

.5261 

5.26 

.6601 

5.92 

.7783 

3.29 

.1909 

3.95 

.3737 

4.61 

.5282 

5.27 

.6620 

5.93 

.7800 

3.30 

.1939 

3.96 

.3762 

4.62 

.5304 

5.28' 

.6639 

5.94 

.7817 

3.31 

.1969 

3.97 

.3788 

4.63 

.5326 

5.29 

.6658 

5.95 

.7834 

3.32 

.1999 

3.98 

.3813 

4.64 

.5347 

5.30 

.6677 

5.96 

.7851 

3.33 

.2030 

3.99 

.3838 

4.65 

.5369 

5.31 

.6696 

5.97 

.7867 

3.34 

.2060 

4.00 

.3863 

4.66 

.5390 

5.32 

.6715 

5.98 

.7884 

3.35 

.2090 

4.01 

.3888 

4.67 

.5412 

5.33 

.6734 

5.99 

.7901 

3.36 

.2119 

4.02 

.3913 

4.68 

.5433 

5.34 

.6752 

6.00 

.7918 

3.37 

.2149 

4.03 

.3938 

4.69 

.5454 

5.35 

.6771 

6.01 

1.7934 

3.38 

.2179 

4.04 

.3962 

4.70 

.5476 

5.36 

.6790 

6.02 

1.7951 

3.39 

.2208 

4.05 

.3987 

4.71 

.5497 

5.37 

.6808 

6.03 

1.7967 

3.40 

.2238 

4.06 

.4012 

.72 

.5518 

5.38 

.6827 

6.04 

1.7984 

3.41 

.2267 

4.07 

.4036 

.73 

.5539 

5.39 

.6845 

6.05 

1.8001 

3.42 

.2296 

4.08 

.4061 

.74 

.5560 

5.40 

.6864 

6.06 

1.8017 

3.43 

.2326 

4.09 

.4085 

.75 

.5581 

5.41 

.6882 

6.07 

1.8034 

3.44 

.2355 

.10 

.4110 

.76 

.5602 

5.42 

.6901 

6.08 

1.8050 

3.45 

.2384 

.11 

.4134 

.77 

.5623 

5.43 

.6919 

6.09 

1.8066 

3.46 

1.2413 

.12 

.4159 

.78 

.5644 

5.44 

.6938 

6.10 

1.8083 

3.47 

1.2442 

.13 

.4183 

.79 

.5665 

5.45 

.6956 

6.11 

.8099 

3.48 

1.2470 

.14 

.4207 

.80 

.5686 

5.46 

.6974 

6.12 

.8116 

3.49 

1.2499 

.15 

.4231 

.81 

.5707 

5.47 

.6993 

6.13 

.8132 

3.50 

1.2528 

.16 

.4255 

4.82 

.5728 

5.48 

.7011 

6.14 

.8148 

3.51 

1.2556 

4.17 

.4279 

4.83 

.5748 

5.49 

.7029 

6.15 

.8165 

3.52 

1.2585 

4.18 

.4303 

4.84 

.5769 

5.50 

.7047 

6.16 

.8181 

3.53 

1.2613 

4.19 

.4327 

4.85 

.5790 

5.51 

.7066 

6.17 

.8197 

3.54 

1.2641 

4.20 

.4351 

4.86 

.5810 

5.52 

.7084 

6.18 

.8213 

3.55 

1.3669 

4.21 

.4375 

4.87 

.5831 

5.53 

.7102 

6.19 

.8229 

3.56 

1.2698 

4.22 

.4398 

4.88 

.5851 

5.54 

.7120 

6.20 

.8245 

3.57 

1.2726 

4.23 

.4422 

4.89 

.5872 

5.55 

.7138 

6.21 

.8262 

3.58 

1.2754 

4.24 

.4446 

4.90 

.5892 

5.56 

.7156 

6.22 

.8278 

3.59 

1.2782 

4.25 

.4469 

4.91 

.5913 

5.57 

.7174 

6.23 

.8294 

3.60 

1.2809 

4.26 

.4493 

4.92 

.5933 

5.58 

.7192 

6.24 

.8310 

3.61 

1.2837 

4.27 

.4516 

4.93 

.5953 

5.59 

.7210 

6.25 

.8326 

3.62 

1.2865 

4.28 

.4540 

4.94 

.5974 

5.60 

.7228 

6.26 

.8342 

3.63 

1.2892 

4.29 

.4563 

4.95 

.5994 

5.61 

.7246 

6.27 

.8358 

3.64 

1  .2920 

4.30 

.4586 

4.96 

.6014 

5.62 

.7263 

6.28 

.8374 

3.65 

1.2947 

4.31 

.4609 

4.97 

.6034 

5.63 

.7281 

6.29 

.8390 

3.66 

1.2975 

4.32 

.4633 

4.98 

.6054 

5.64 

.7299 

6.30 

.8405 

3.67 

1.3002 

4.33 

.4656 

4.99 

.6074 

5.65 

.7317 

6.31 

.8421 

3.68 

1.3029 

4.34 

.4679 

5.00 

.6094 

5.66 

.7334 

6.32 

.8437 

3.69 

1.3056 

4.35 

.4702 

5.01 

.6114 

5.67 

.7352 

6.33 

.8453 

3.70 

1.3083 

4.36 

'.4725 

5.02 

.6134 

5.68 

.7370 

6.34 

.84(59 

3.71 

1.3110 

4.37 

.4748 

5.03 

.6154 

5.69 

.7387 

6.35 

.8485 

3.72 

1.3137 

4.38 

.4770 

5.04 

.6174 

5.70 

.7405 

6.36 

.8500 

3.73 

1.3164 

4.39 

.4793 

5.05 

.6194 

5.71 

.7422 

6.37 

.8516 

3.74 

1.3191 

4.40 

.4816 

5.06 

.6214 

5.72 

.7440 

6.38 

.8532 

3.75 

1.3218 

4.41 

.4839 

5.07 

.6233 

5.73 

.7457 

6.39 

.8517 

3.76 

1.3244 

4.42 

.4861 

5.08 

.6253 

5.74 

.7475 

6.40 

.8563 

3.77 

1.3271 

4.43 

.4884 

5.09 

.6273 

5.75 

.7492 

6.41 

.8579 

3.78 

1.3297 

4.44 

.4907 

5.10 

.6292 

5.76 

.7509 

6.42 

.8594 

3.79 

1.3324 

4.45 

1.4929. 

5.11 

.6312 

5.77 

.7527 

6.43 

.8610 

3.80 

1.3350 

4.46 

1.4951 

5.12 

.6332 

5.78 

.7544 

6.44 

.8625 

3.81 

1.3376 

4.47 

1  .4974 

5.13 

.6351 

5.79 

.7561 

6.45 

.8641 

3.82 

1.3403 

4.48 

1.4996 

5.14 

.6371 

5.80 

.7579 

6.46 

.8656 

3.83 

1.3429 

4.49 

1.5019 

5.15 

.6390 

5.81 

-  .7596 

6.47 

.8072 

3.84 

1.3455 

4.50 

1.5041 

5.16 

.6409 

5.82 

.7613 

6.48 

.8687 

3.85 

1.34H1 

4.51 

1.5063 

5.17 

.6429 

5.83 

.7630  ' 

6.49 

1.8703 

3.86 

1  .3507 

4.5'J 

1.5085 

5.18 

.6448 

5.84 

1.7047 

6.50 

1.8718 

Voluine,  uensltjr,  and  Pressure  of  Air  at  Various 
Temperatures.    (D.  K.  Clark.) 


Volume  at  Atinos. 

Pressure  at  Constant 

Pressure. 

Density.  Ibs. 

Volume. 

Fahr. 

per  Cubic  Foot  at 
Atmos.  Pressure. 

Cubic  Feet 
in  1  Ib. 

Compara- 
tive Vol. 

Lbs.  per 
'  Sq.  In. 

Compara- 
tive Pres. 

0 

11.583 

.881 

.086331 

12.96 

.881 

32 

12.387 

.943 

.080728 

13.86 

.943 

40 

12.586 

.958 

.079439 

14.08 

.958 

50 

12.840 

.977 

.077884 

14.36 

.977 

62 

13.141 

J.OOO 

.076097 

14.70 

.000 

70 

13.342 

1.015 

.074950 

14.92 

.015 

80 

13.593 

1.034 

.07a565 

15.21 

.034 

90 

13.845 

.054 

.072230 

15.49 

.054 

100 

14.096 

.073 

.070942 

15.77 

.073 

no 

14.344 

.092 

.069721 

16.05 

.092 

120 

14.592 

.111 

.06^500 

16.33 

.111 

130 

14.846 

.130 

.067361 

16.61 

.130 

140 

15.100 

.149 

.066221 

16.89 

.149 

150 

15.351 

.168 

.065155 

17.19 

.168 

160 

15.603 

1.187 

.064088 

17.50 

.187 

170 

15.854 

1.206 

.063089 

17.76 

.206 

180 

10.106 

1.226 

.062090 

18.02 

.226 

200 

16.606 

1.264 

.060210 

18.58 

.264 

210 

16.860 

1.283 

.059313 

18.86 

.283 

212 

16.910 

1.287 

.059135 

18.92 

1.287 

216 


Volumes,  Ulean  Pressure*  per  Stroke,  Temperatures,  etc.. 
in  the  Operation  of  Air-compression  from  1  Atmosphere 
and  60°  Fahr.  (F;  Richards,  Am.  Mack.,  March  30,  1893.) 


45 


65 


O 
1 
0 

1 

2 

3 

4 

5 
10 
15 
202.36 
25 
30  3.04 
353.3S1 
40  3.721 


1 

1.068 
1.136 
1.204 

K34 

I  68 


4.061 


504.401 
55  4.741 
605.081 


0.423 


705.762 
6.102 


i! 

•5^ 


l 

9363 

.8803 
,8305 
7861 
7462 
,5952 
495 
,4237 
3703 
3289 
2957 
2687 
2162 
2272 
2109 

1844 
1735 
1639 


1 

.95 
.91 

.876 

.84 

.81 

.69 

.606 

.543 

.494 

.4538 

,42 

393 

37 

,35 

331 

,3144 

301 

288 

,276 


0.00. 

p  u  C 


0 
.96 
1.87 
2.72 
3.53 
4.3 
7.62 
10.3:}  11 


14.59 

16.34 

17.9221.6 

19.3223 

20.5725.! 

21.6927 

22.7629 

23  78  30 

24  7532 

25  07 


26.55 


35.2 


60° 

71 

80.4 

88. 

98 
106 
145 
178 
207 
:.'34 
252 
281 
302 
321 
339 
357 
375 
389 


85!  6, 
90!  7 
95  7 
100'  7 
105!  8 
110  8 
115!  8 
120,  9 
125  9 
130  9 
135  10 
140  10 
145  '10 
15011 
160  11 
170  12 
180  13 
190  13 
200  14 


USEFUL  TABLES. 


217 


Mean  and  Terminal  Pressures  of  Compressed    Air  used 
Expansively  for  Gauge-pressures  from  60  to  IOO  Ibs. 

(Frank  Richards,  Am.  Mack.  April  13,  1893.) 


Initial 

Pres- 

60. 

70. 

80. 

90. 

100. 

sure. 

"ofc 

a  ,  2 

1,2 

,    2 

1  .  2 

<D 

a     % 

"3     2 

3        2 

-5     ;> 

a. 

"3      ® 

«j  O 

§^3 

-2  -I  3 

§  U  3 

•2  <L  3 

as  u  3 

•2  i.  3 

«J  u  3 

.2  t,  3 

§  —  3 

•s.=.  ! 

"o  3 

D  ••-   M 

i^i 

•B^ii 

C  ••T  </3 

jg<  1 

|«5  ft 

»«g 

«««  S 

£<  % 

go 

ft 

E"      ft 

2 

H    ft 

ft 

£    Q. 

ft 

H     ft 

ft 

E-      ft 

.25 

23.6 

10  65 

28.74 

I2.O7 

33.89 

13.49 

39  04 

14.91 

44.19 

1.33 

.30 

28.9 

ltf.77 

34.75 

6 

40  61 

2.44 

46  46 

4*27 

53.82 

6  11 

tt 

32.13 

.96 

38.41 

3.09 

44.69 

5  22 

50.98 

7  35 

57  26 

9  48 

.35 

33.66 

2.33 

40.  15 

4.38 

46.64 

6.66 

53.13 

895 

59  62 

11.23 

% 

35.85 

3.85 

42  63 

6.36 

49.41 

7.88 

56  2 

11.39 

62  98 

13.J59 

.40 

37.93 

5.64 

44.99 

8.39 

52.05 

11.14 

59  11 

13.88 

66  16 

16.64 

,45 

41.75 

10.71 

49.31 

12.61 

56.9 

15.86 

64  45 

19.11 

72.02 

22.36 

.50 

45.14 

13.26 

53.16 

17 

61.18 

20  81 

69.19 

24  56 

77.21 

28.33 

.60 

50.75 

21.53 

59.51 

26.4 

68.28 

31  27 

77.05 

36.14 

85.82 

4)  0) 

% 

51.92 

23.69 

60.84 

28.85 

69.76 

34.01 

75.69 

39.16 

87.61 

44.3? 

7& 

53.67 

27.94 

6283 

33.03 

71.99 

38.68 

81  14 

44  :# 

90.32 

49  97 

.70 

54.93 

30.39 

64  25 

36  44 

73.57 

42.49 

82  9 

48.54 

9*.  22 

54.59 

.75 

56.52 

35.01 

66.05 

41.68 

75.59 

48.35 

85.12 

55.02 

94.66 

61  69 

.80 

57.79 

39.78 

67.5 

47.08 

77.2 

54.38 

86.91 

61.69 

96.61 

68.99 

% 

59.15 

47.14 

69.03 

55.43 

78.92 

63.81 

88.81 

72. 

9S.7 

80  28 

.90 

59.46 

49.65 

69.38 

58.27 

79  31 

66  89 

89.24 

75.52 

99.17 

8782 

The  pressures  in  the  table  are  all  gauge-pressures  except  those  in  italics 
which  are  absolute  pressures  (above  a  vacuum). 


218 


TABLES. 


R. 

I 

K 

Pm 

P^ 

R 

i 

R. 

1% 

p, 

2.  0 

.05" 

/9<?8 

5 

.    3. 

.5218 

1  8 

.055" 

.  2.161 

4-^4 

•   225" 

.  5^o8 

I  6 

.  06* 

.  ^35-8 

4. 

.  2  5 

.  $^6S 

I  5" 

.  0  66 

.  24/£ 

3.63 

.2/5 

.  £3od 

1  4 

.  07  i 

.  25^^ 

3.33 

.  3 

>66^5 

13.35 

.  0/5- 

.26, 

3 

.333 

.^*|3 

1  5 

.  077 

.  iftz 

2.86 

.   3  5" 

•  7«7' 

1  2, 

.  o»3 

.  2C|.o4- 

Z.66 

.37^ 

•7^ 

1  1 

•  09  i 

.  So8c| 

*   Fo 

•4 

.?664 

1  0 

.  < 

.  33cS 

a.  a^t 

.  ^*  J 

.8095- 

9 

.Ml 

.  355-2 

^. 

»   5- 

.  846S 

8 

.  ia5 

.  aa^cj 

1.  8Z, 

,   5  5- 

.  87^6 

7 

.  I  ^*  3 

.  ^Al 

1.66 

.  6 

.  Cjo66 

666 

.  /  $• 

.  434/ 

\  60 

.  62$ 

•  9  '  87 

6 

.   166 

.  A^53 

I.5-4 

.  6  $• 

.c,i^2 

S./I 

..75- 

.  ^8  07 

Ma 

.67? 

.  q^  oS 

T^U 

*.  of  MeaM  Absolute  Prcssu 
Various  De^reeiaf  IsotUrmal  Exf 

—  for 

>avt&«on  —  — 

In  this  Table.  

P,    is  tk«.  Absolute   Pressure.   aV  wKick  Sfcam  cv\Ttvv$  H\t    Cjli'wckr, 
Pm    i&   Vive.   Corr*ipon<i»'na     Mt.av\  Absolute  Pre.6Su.re.  , 
R~  »S    Hvt    Hate   of  ExpaMbtow,    .'....  Hyc  Rati.  of  rt»e,  UV«a  v«U^e.  of 

C^lmcUT  ,  tncUta^   Ckft,r«twc».,  U  UUL  VoUm*  of  Lwi  SUam^VUi^  £lexr«M« 
±      inclicaHs    Vkt.  |»o»»t-  »f  C«*.«ff.  .*.«.%.  R*tt;  »f  *e-  W*l  v»l«*mi.of  Uv 
^^  Sr«.cuvt    fo    vUt    Uh«x\    Voli^MAC    of  C.vliH^«,y    a.V  hln.  twi  »f  riia.  Stv*>C«-     - 

USEFUL  TABLES. 


219 


Nown'w<*l 

us,-a«. 
j>io.  w\*r«* 

l,ck»»   

Actuo.1 
OwrisicU 

J3  1  A  wv«.rar 
lnek«&  

N  ow>  i  'y\a>\ 
We.jkK 
^«T  ro^r 

—  Lbi     

Number    »f    TKyea«U 
J»ar    twtK 
«f?    Scye.w 

3. 

M 

'.a.  ^,^ 

14 

M 

M 

^  «^ 

1    f 

2,-i 

«j 

3-  i  3 

1  4 

*l 

3 

3.  *  5      . 

i  4 

3- 

*| 

^      1     0 

I  f 

»•* 

M 

445 

I  4 

3.Jj 

3| 

4  78 

1  4 

*.| 

4 

5".  5-6 

I  4 

4 

4^ 

6. 

1  5 

4-i 

4i 

^.36 

I  4 

*i 

5j 

f.?3 

1  4 

4-| 

5- 

?•  a  o 

1  ^ 

^ 

5-i 

S.io 

Ml 

*3 

S.i 

a  6*, 

i  f 

^•f 

6 

)   €>  .  4  6 

1  ^ 

6-4 

^1 

1   I.  Sfl 

I  4 

*I 

7 

12.3^ 

1  4 

7-i 

7f 

13-  ^^ 

1  4 

>-f 

1 

1  5-  A  1 

LLJ 

a.. 

H[ 

;  ^.  07- 

/Li 

8,f 

q 

1  /.  tf  o 

LL4 

vf 

1     0 

A  1  •  cf  o 

LL4 

"f 

1      I 

i6.7^ 

i  .  i 

i«  f 

1    2. 

3o.35 

i  -i.i 

iai 

I  3 

33.^8 

nj 

I  3  4 

i  4 

4^.  c  ^ 

Mi 

"»  k 

i  S 

A  7    6  * 

i  »-k 

is  i 

I  6 

5*1.  ^7 

...i 

—  .Lisf    «f    Well  Casiwa   

USKFUI,  TABLES. 


9  Butt  -WeUed    

Nominal 

Actual 

—  1  \\cUti  .  _ 

_TK;-:z_ 

—  Lbs  — 

of     Straw 

a 

.  4 

.  •  <  • 

.  2<f 

2-7 

4 

.  5-4 

.068 

•A2. 

1   8 

\ 

.   67 

.0^1 

.  5*6 

1    £ 

I 

•    84 

.ioc) 

.  84 

»  ^ 

1 

/.  OS" 

.113 

1.12 

1  4 

1 

I.  3l 

>   »  3  4 

/  .<7 

*    '     k 

'  i 

1-66 

.1/10 

2.a4 

11  i 

Lap.  Wel4cd     

Nominal 

1  *S,'d  a 

Hi 

-fci±T. 

Hf_ 

Mt%f*u»«*^ 

A 

l.<* 

,  i  4  «r 

2.68 

'  •  •  z. 

z 

2.37 

.  /  r^ 

3.61 

'  '-i 

*  i 

2.87 

•  i«4 

^.7^ 

* 

3 

d.  5- 

.  ii  7 

7.^-4 

B 

3   i 

4 

•  2*6 

<^ 

* 

4 

/I.5- 

•  *37 

|0.  66 

8 

*  i 

5" 

.  ^47 

12.34 

9 

5 

,rtf 

.  2.5-cj 

•I4..S-0 

B 

2 

^.^2. 

.  a.  a  o 

\9.76 

8 

7 

7  <x 

•  3*1 

m.j 

8 

3 

«.6Z 

.  aaa. 

48  1  & 

8 

9 

q.  «8 

•  »4^ 

33.70 

8 

/    0 

1  0.75 

.  3^<J 

4o 

8 

i  l 

1  1-  7«" 

.  J  7  f 

45 

8 

)  2. 

12.7^ 

.375^ 

y 

8 

1  3 

I/* 

.  3/5- 

54 

8 

1  4 

IS 

.  3/5" 

55 

8 

I-5" 

16 

.  »7«- 

4^i 

8 

—    List     of      SlTtawt,    AiV     -vw*    Ware/     Pi>*S  .    

INDEX. 


PAGE 

Air  Compressors— General  Remarks 81 

Air  Engines , 38 

Air  Engines,  Exhaust  Temperatures  and  Reheating 50 

Air  Receivers 182 

Available  Work  at  Complete  Expansion,  Curve  of. 30 

Available  Work  at  Full  Expansion,  Table  of. 31 

Blacksmith  Tools 186 

Capacity  of  Compressors 84 

Calculation  of  H.  P.  of  Water,  Table  of 207 

Circumferences  and  Areas  of  Circles 191 

Column  Mountings 180 

Compressed  Air,  General  Principles 3 

COMPRESSORS— 

Combined  Duplex  Steam   Actuated  and  Shaft-driven    Com- 
pressors, Class  G 105 

Compound  Corliss  Actuated  Compressors,  Class  J 110 

Direct  Acting  Steam  Actuated  Duplex  Compressors,  Light 

Duty,  Class  L 119 

Duplex  Steam  Actuated  Compressors,  Class  A 80 

Duplex  Shaft-driven  Compressors,  Class  D 95 

Duplex  Tandem  Sectional  Shaft-driven  Compressors,  Class  E.    99 

Light  Duty  Compressor  or  Vacuum  Pump,  Class  K 117 

Single  Steam  Compressors,  Class  B 91 

Single  Steam   Actuated  Compressors,  Self-contained   Type, 

Class  C 93 

Single  Shaft-driven  Compressors,  Class  F 102 

Single  Corliss  Actuated  Compressors,  Class  1 113 

Steam  Actuated  Vertical  Compressors,  Class  H 108 

Steam  Actuated  Single  Air  Compressors,  Class  M . .  121 

Consumption  of  Air 40 

Consumption  of  Air,  Single  Cylinder  Automatic  Engines 41 

Consumption  of  Air,  Compound  Automatic  Engines. 42 

Consumption  of  Air,  Single  Cylinder  Corliss  Engines 43 

Consumption  of  Air,  Compound  Corliss  Engines 44 

Consumption  of  Air,  Corliss  Compound  Pneumatic  Motors,  Table 

of i 51 

Consumption  of  Air  for  pumps 01 

Consumption  of  Air,  Rock  Drills 85 

Decimals  of  a  Foot  per  Each  Sixty-fourth  of  an  Inch 202 

Decimals  of  an  Inch  for  Each  Sixty-fourth 206 

Difference  of  Level  in  Use  of  Compressed  Air 35 

Difference  of  Level  in  Use  of  Compressed  Air,  Table  of 37 

Equation  of  Pipes 212 

Expansion  ot  Air 45 


INDEX. 

PAGE 

Fifth  Roots  and  Fifth  Powers 191 

General  Hints 178 

Hyperbolic  logarithms 213 

Indicated  Horse  Power  to  Compress  Air 56 

Indicated  Horse  Power  to  Compress  Air,  Curve  for 57 

Loss  of  Pressure  in  Pipes .. 21 

Loss  of  Pressure  through  Bends 33 

Loss  of  Pressure  through  Bends,  Table  of 34 

Loss  of  Head  in  Pipes!  by  Friction 208 

Lubricators  and  Lubricants 187 

Mean  and  Terminal  Pressures  of  Compressed  Air 217 

Mean   Absolute  Pressures  Tor   Various  Degrees  of  Isothermal 

Expansion,  Table  of 218 

Mean  Effective  Pressures,  Curve  of 58 

Pneumatic  Governors 127 

Pneumatic  Hoist 52 

Pneumatic  Locomotive ..     70 

Pneumatic  Plant  at  Grass  Valley 134 

Pneumatic  Torpedo  Plant  at  Presidio,  S.  F 140 

Power  Transmission  by  Compressed  Air 71 

Pressure  in  Vertical  Pipes 59 

Quantity  of  Air  Compressed  per  Indicated  Horse  Power 53 

Quantity  of  Air  Compressed  per  Indicated  Horse  Power,  Curve 

for 54 

Reheater 48 

Refrigeration  by  Compressed  Air 63 

Rix  Patent  Hose  Couplings 180 

ROCK  DRILLS— 

Rock  Drills 158 

Rock  Drills,  Rix,  Table  of 170 

Rock  Drills,  Giant,  Table  of 171 

Rock  Drills,  Plug  and  Feather 176 

Sheet  Iron  Hydraulic  Pipe,  Table  of. 210 

Squares,  Cubes,  and  Reciprocals 195 

Tripod  Mountings 165 

Temperatures,  Centigrade,  and  Fahrenheit 200 

Volume,  Density,  and  Pressure  of  Air  at  Various  Temperatures.  215 

Volumes,  Mean  Pressure  per  Stroke,  Temperatures 21(5 

Well  Casing,  List  of 219 

Wrought  Iron  Pipe,  List  of 220 


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